Category: Physics Notes PPT

When the motion of a body follows a circular path around a fixed point, it is known as circular motion. Here, uniform circular motion is a particular kind of circular motion where the motion of the body follows a circular path at a constant/uniform speed. The body has a fixed central position and so remains at an equal distance from it at any known point.

When an object moves around in circular motion, there are many distinguishing factors to consider. 

Explanation through an Example

You have a ball attached to a string, and you move it uniformly over a circular motion; then, two interesting observations can be made.

1. The speed of the ball remains constant, tracing the circle over a fixed center point.

2. The ball remains in motion changing its direction constantly. As such, one can opt to stay on a circular path; the ball must change its direction in a constant manner.

We can gain an important observation from the 2nd point. According to Newton’s first law, there will be no acceleration without a net force. As such, there must be a force entangled with the circular motion. Nevertheless, for a circular motion to happen, the object must be acted by a net force, thereby resulting in the change of direction otherwise known as centripetal force.

Imagine that your friend has been kidnapped by aliens, and they have kept him in an object moving in a circular motion. You will be able to save him, only after understanding the mechanism. This page will help you with the basics of circular motion.

From the above-mentioned theory, as long as your friend is in the field of circular motion, it will continue to follow the circular path. The moment the attachment breaks or you let go, the centripetal force stops acting, and your friend will be detached from the object. Then it will be easier for you to rescue your friend. 

Types of Circular Motion

There are two kinds of circular motion that can act upon a body in motion:

1. Uniform circular motion or UCM, 

2. Non-uniform circular motion

In the case of uniform circular motion, the angular speed & acceleration remains constant, whereas the velocity differs. However, in a non-uniform circular motion, both the angular speed and velocity change.

Uniform Circular Motion Formula

Consider a particle moving in a circle. It will have some acceleration acting at the center. This makes it move around the center position. As acceleration is perpendicular to the velocity, it only changes the direction of velocity, and the magnitude remains unchanged. This is the reason the motion is called uniform circular motion. This is otherwise called centripetal acceleration, and the force that acts towards the center is known as centripetal force.

So, the centripetal force is the force acting on a body over a circular path. This points toward the center of the body in motion.

Considering the uniform circular motion, the acceleration is:

[ ar = v^{2}r = omega ^{2} r]

where,

a=acceleration, r=radius, v=velocity of the object, ω=angular speed

If the mass of the particle is m, from the 2nd law of motion, you can find that:

[ F = ma ]

[Mv^{2}r = momega ^{2}r]

So, if a particle moves in a uniform circular motion:

• Its speed is constant

• Velocity changes at every instant

• No tangential acceleration acts on the body

• Radial (centripetal) acceleration = [ omega ^{2}r ]

• v=ωr

In the case of non-uniform circular motion, the tangential acceleration increases/decreases resulting in the acceleration to be the sum of tangential and radial acceleration.

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Uniform Circular Motion Examples

Below is the following example of uniform circular motion:

1. An example of uniform circular motion is the motion of artificial satellites around the earth. The satellites stay in the circular orbit around the earth due to gravitational force from the earth.

2. around the nucleus the motion of electrons. The perpendicular movement to the uniform magnetic field of electrons.

3. The blade of windmills motion.

4. With a circular dial, the tip of the second hand of a watch shows uniform circular motion.

5. A rope tied to the stone and being swung in a circular motion.

6. A curve in a road, a car turning through.

7. A gear-train inside turning a gear.

8. Clock hand motion.

9. Bicycle wheels of motion.

What is the concept of Uniform Circular Motion?

Uniform circular motion will always be used to describe the magnitude
of the velocity. The direction of velocity will change at a constant rate from every place. The object’s route will be in the shape of a circle, which represents it. The object will be completed after making multiple journeys around the path in the same length of time at the same spot.

The word circular refers to mobility along a curved path. Circular uniform motion is defined as an item moving along a circular path while covering the same distance along the circumference in the same time interval. The speed remains constant in such continually shifting motions.

The tangential speed will be constant at all points along the circumference in a uniform circular motion. The tangential velocity vector is tangent at all points around the circumference. As a result, the acceleration vector always points towards the center of the circle produced by the object’s motion. Because it is at a given radius from a central point, or as a centripetal acceleration, or as a radical acceleration, which indicates that it is central seeking.

What are the learning objectives for Uniform Circular Motion?

You will be able to understand the following by the end of this section:

• Of an object moving on a circular path solution for the centripetal acceleration.

• Of a particle executing circular motion using the equations of circular motion to find the velocity, speed, and acceleration positioning.

• Resulting from non-uniform circular motion explaining the differences between tangential acceleration and centripetal acceleration.

• Find the total acceleration vector and evaluate tangential and centripetal equations in a non-uniform circular motion.

A specific type of motion in which an object travels in a circle with a constant speed at a particular time given is known as uniform circular motion. Some examples are a propeller spinning at a constant rate at any point is executing the circular uniform motion, the hour’s hand, and the second minute of a watch. To watch all this we must know how to analyze the motion in terms of vectors at a particular period. Although the rotation rate is constant, remarkably, points on these rotating objects are accelerating.

The attribute of a current-carrying closed-loop that causes an electromotive force to be generated or induced by a change in the current flowing via it. Such an attribute is called the inductance.

On This Page, We’ll Learn About the Following:

Inductor

An inductor is a coil of wire cloaked around a magnetic material.

Current flowing via the inductor generates a magnetic field that does not change, as it is trying to oppose the change in the flow of current which means the current flow remains constant inside the inductor. 

The inductor won’t generate any forces on the charged particles flowing via it. In such a case, the inductor just behaves like a normal wire.

The current flow is opposed by the resistance, and the time comes when there comes a 

current decay (decline). The larger the resistance, the faster the current will decline.

On the other hand, the larger the inductance of the inductor, the slower the current will decay.

What is Inductance?

The inductance is the ability of an inductor or any current-carrying conductor to oppose the change in the current flowing through it. The inductors do this by generating a self-induced emf within itself (Faraday’s law of induction) as a result of their changing magnetic field. 

S.I. Unit of the Inductor

The S.I unit of the inductor is Henry H

MKS unit is Kg m² s⁻² A⁻²

Where one Henry is equal to the one-kilogram meter squared per second squared per ampere squared.

What is Self – Inductance?

Inductance is also called self-inductance. When a current is established in a closed conducting loop, it creates a magnetic field. This magnetic field has flux produced in an area of the closed-loop. If the current varies with time, the flux via the loop also changes. Hence an EMF is induced in the loop. Such a process is called self-induction.

The magnetic field at any point due to current is proportional to the current. The magnetic flux in an enclosed area of the conductor can be represented as,

φ  ∝ i  ⇒ φ = L i

Where L is a proportionality constant and is called the coefficient of self-inductance or simply self-inductance of the loop.

The inductance in the coil (Fig.1) depends on the number of turns, area of cross-section, and nature of the material of the core on which the coil is wrapped.

If i =1,  φ = L x i  or  L = φ

Therefore, the coefficient of self-inductance is numerically equal to the amount of magnetic flux linked with the coil when unit current flows through the coil.

From Faraday’s law of induction, any variation in the magnetic field generates emf, given by,

E =  –  dφ (t) / dt  = – L di / dt

The negative sign indicates that the changing current induces a voltage in the conductor and this induced voltage is in a direction that tends to oppose the change (increase or decrease) in the electric current (Lenz’s law) is called the back EMF.

Inductance for a Long Solenoid

The inductance of a solenoid is given by,

B = μ₀ N I / L

The magnetic flux density can be obtained by multiplying the B with cross-sectional area A, we get,

φ = B xA = μ₀ N x i x A / l….(1)

Since total magnetic flux inside the coil = flux via each turn x total number of turns. 

φ = B xA = μ₀ N x N i x A / l….(2)

Where μ₀ is the magnetic constant or absolute magnetic permeability of free space/air forms the core of the solenoid.

We know that

φ  = L i….(3)

From (2) and (3) we get,

L i =  μ₀ N x N x A xi / l x N we get,

L = μ₀ N² x A/ l

μ = μ₀ . μr

When the core is of any other magnetic material μ₀ is replaced by 

μr (relative magnetic permeability).

Here, we Conclude the Following Things,

S.I. Unit of Inductance

The S.I. unit of self-inductance is weber/ ampere or volt-second/ ampere. 

It is also denoted by Henry (H), named after an American scientist named Joseph Henry. 

Where Henry is the amount of inductance that generates a change of one volt and when the current is varying at the rate of one ampere per second.

Note: All conductors have some inductance, which may have either desirable or detrimental effects in electrical circuits and it depends on the geometry of the current path and on the magnetic permeability of the materials.

The ferromagnetic material tends to have a high inductance because of the flow of large amounts of electric flux (total magnetic field) through the conductor produced by a current flowing through it increases the inductance in that conductor.

Inductor Working Principle

When ac current is applied to the inductor coil, its own current changes, causing its own magnet to change, creating an electromotive power. This condition is called self-inductance. The direction of the self-induced current is always affected. When the alternating current increases, the direction of the self-inductance current is opposite to that of the AC current. When the AC current is weak, the direction of the self-inductance current is the same as that of the alternating current, which has a blocking effect.

• Self-Induction- When the current flows into the coil, a magnetic field is produced around the coil. As the current in the coil changes, the surrounding magnetic field also changes accordingly. This change in a magnetic field can cause the coil itself to generate electromotive energy (EMF is used to represent the terminal voltage of the active power of the active components).

• Mutual Inductance- If two coils of an inductor are close together, the magnetic field conversion of one coil will affect the other, and this effect is mutually beneficial. Its size depends on the degree of interaction between self-inductance and the two coils. The components formed by this policy are called mutual inductors.

Factors affecting Inductance in a Circuit

The following factors affect inductance in a circuit

• The Number of Wires Transforming into Coil – The greater the amount of cable twist on the coil, the greater the inductance. Slight twisting of the cable to the coil results in a small inlet. Most cable coils show a large amount of magnetic field in a given number of current coils.

• Coil Location – The larger the coil area, the greater the inductance. The location of the small coil leads to the small entrance. The large coil area exhibits minimal resistance to the formation of magnetic field flux, with a given amount of field strength

• Length of the Coil – When the coil length is longer, the inductance decreases. The shorter the coil length, the greater the inductance.

Summary

With the change in the magnetic flux, induced emf is a must, but induced current will only appear only when the circuit is closed.

An Inductor is equivalent to a short circuit to DC, because once the storage phase has been completed, the current, i, that flows through is stable, no emf is induced. So the inductor behaves like a normal wire where Resistance R is zero

We often visit a dairy to buy milk and ask the shopkeeper to provide us with some litres of milk. Have you ever wondered what this “litre” signifies? It is the Volume and litre is one of its many Units. Here has provided for you a write-up on Volume, its various Units and their interConversion. First, let’s start by understanding what Volume is.  

You know that Volume is the space occupied by a state of matter. So, what is the SI Unit for Volume considered for measuring it? Well! The SI Unit for Volume is m³. However, many other Units are employed for the Volume in Physics. This page discusses the Units of the Volume list in detail.

The Volume is a basic physical quantity, we consider it a derived quantity and it expresses the three-dimensional proportions of an object.

So, we understand that the SI Unit of Volume in Physics is quantified by using the SI derived Unit, the cubic metre.

Volume in Physics

Volume is the amount of three-dimensional space enclosed by a closed surface in terms of numerical value.

For example, the space that a substance can be Solid, liquid, gas, or plasma, or any space-occupying shape. 

The Volume of a container is considered to be the capacity it can hold; i.e., the amount of fluid, a gas, or a liquid that the container can hold, rather than the amount of space the container itself displaces, just like Buoyant force in the water. 

Points to be Noted

3-D mathematical shapes are also assigned Volumes. Volumes of shapes, like the regular, straight-edged, and circular shapes can be easily calculated by using arithmetic formulas. 

Volumes of complex shapes can be calculated by using integral calculus only if the formula exists for the shape’s boundary. 

1-D s like lines and 2-D shapes, such as squares are allotted zero Volume in the three-dimensional space.

The Volume of a Solid

The Volume of a Solid, either regularly or irregularly shaped, can be determined by fluid displacement. 

Where the displacement of liquid is used for calculating the Volume of a gas. The combined Volume of two substances is always greater than the Volume of just one of the substances (liquid or gas). However, sometimes it happens that one substance dissolves in the other, and in these cases, the combined Volume is not additive.

Units of Volume List

Volume measures capacity. So the SI Unit of Volume is a Unit for measuring the capacity or the proportions of an object or space. The Unit m³ is mostly used to specify the Volume of substances or a liquid (fluids). 

However, students must keep in mind that mass and Volume are two different physical quantities. While the Unit of Volume is an interesting topic, so, let’s have a look at what Units are used all over the world below in a tabular form:

Volume in Thermodynamics

In the field of Thermodynamics, the Volume of a system is a significantly extensive parameter for describing the state’s thermodynamic state. 

The specific Volume is an intensive property, it is the Volume of the system per its Unit. 

Volume is a state function and is independent of some thermodynamic properties like pressure and temperature. 

For an ideal gas, the Volume is related to the pressure and temperature, as per the ideal gas law.

Volume Units Conversion

Any Unit of length gives a derived SI Unit of Volume, such as the Volume of a cube that has sides of a given length in metres. 

A cubic centimetre or cm3 is the Volume of a cube whose sides are one centimetre, 1 cm in length.

In the International System of Units or SI, the standard Unit of Volume is the cubic metre (m3). 

In the metric system, the Unit of Volume also includes the litre (L), where one litre is equal to the 10-centimetre cube. 

Therefore, 1 litre = (10 cm)3 = 1000 cubic centimetres 

= 0.001 cubic metres,

So,

1 cubic metre is equal to 1000 litres.

Small amounts of liquid are measured in millilitres Units, where

1 millilitre = 0.001 litres or 1 cubic centimetre.

In the same way, large amounts are measured in megalitres, i.e.,

1 million litres = 1000 cubic metres or 1 megalitre.

Various traditional Units of Volume are still in use, including the following Units of Volume list:

1. cubic inch, 

2. the cubic foot, 

3. the cubic yard, 

4. the cubic mile, 

5. the teaspoon, 

6. the tablespoon, 

7. the fluid ounce, 

8. the fluid dram, 

9. the gill, 

10. the pint, 

11. the quart, 

12. the gallon, 

13. the minim, 

14. the barrel, 

15. the cord, 

16. the peck, 

17. the bushel, 

18. the hogshead,

19. Drams grill

20. Bushels

21.  Pecks

22. the acre-foot, and 

23. the board foot

has also provided a detailed introduction to the topic of Volume. If you are finding it difficult to understand this topic directly, it is suggested you refer to the topic of Volume formulas before proceeding with it.    

Conclusion

After reading this article you are well aware of various Units of Volumes, their interConversions and traditionally used Units of Volume. Studying this write-up has taught you how significant Volume and its Units are. These Conversion formulas come in handy at many places in exams and also in practical life. Thus, you have to give your best to understand this topic and try to apply it at various places to ensure you master it. 

Now, how does an electromagnet work? It works on the principle of an electric current producing a magnetic field. This magnetic field is generated by an electric current that forms circles around the electric current.

 

If a wire is carrying an electric current is formed into a series of loops, the concentration of the magnetic field can be changed within the loops, by varying it. The magnetic field can be strengthened by wrapping the wire up and around the core of the magnet. The atoms of magnetic materials, such as iron, nickel, and cobalt, behave like tiny magnets.

 

When we increase the concentration of the magnetic field, the current that is flowing around the core increases and the number of aligned atoms increases which results in stronger a magnetic field Sooner or later, all of the atoms that are supposed to be aligned will be aligned. At this particular point when the atoms are aligned with each other, the magnet is said to be saturated, and it experiences an increasing electric current flowing around the core. This no longer affects the magnetization of the core itself.

 

How do Electromagnets Work?

There are four primary forces in physics, and one of them is called electromagnetism. It is a combination of two forces, electric forces, and magnetic forces. Let us see how these forces can contribute to the electromagnets.

 

These two forces are very different, but when they come together with the form of electromagnetic forces. They complement each other very well and is used in many days to day applications. 

 

The two essential elements that make up this force are charges like protons and electrons. When they are stationary, they produce electric forces, which can be attractive or repulsive forces between charged particles. But when electrons and protons are moving, they produce magnetic forces which can be a force of attraction or repulsion between the charged particles that are formed because of the motion of the charged particles.

 

When charges, like electrons or protons, are stationary, they produce electric forces or an attractive or repulsive force between charged particles. But when electrons or protons are moving, they generate magnetic forces or an attractive or repulsive force between charged particles due to their motion. 

 

Now, Where are these Electromagnets Used?

Let us take a look at the everyday conventional uses of electromagnets. Electromagnets can be used in powerful tools for lifting and other heavyweight instruments.

 

Unlike a regular magnet, you can switch on and off an electromagnet. They only work with n external power source. An electromagnets strength can be changed according to the amount of current flowing in the wires; it can be altered accordingly. Electromagnets are used by large Businesses that use machinery to do heavy lifting like lifting cars or to move it to another location or even by scrapyards to separate iron and other ferrous metals from nonferrous materials.

 

Japan is currently testing a 320 kilometer per hour (200 miles per hour) levitating train that uses electromagnets to hover and move around the entire place. The U.S. Navy also performs high tech experiments with a futuristic electromagnetic rail gun weapon. The Navy has also used an electromagnetic catapult that has been to launch planes off carrier decks.

 

Electromagnets and Induction

What is induction? It is the phenomenon that takes place when a wire that’s near to a changing magnetic field produces electric current. Electric motors, transformers, and power generators all work because of this popular phenomenon called induction. Transformers are critical in this electrical transmission because they are used to step the voltage up or down as needed during its course to the consumers. Electric motors also have the ability to turn electric current into mechanical power in all manner of equipment. This includes toy cars, real cars, washing machines, and power tools. The power generators work like electric motors, but in the other way around: they turn rotary motion into electric power. The rotary motion can come from machinery like windmills, steam turbines or any other sources.

 

Electromagnets Used in Other Common Devices

Although you may never see some electromagnets, they are often hidden in many electronic products you use in your day to day life. Press a doorbell, for example, and the electric current creates a magnetic field that attracts a ringer which strikes the bell. Relays are individual electromagnets that usually function like automatic electrical switches. They are found in a variety of consumer and commercial applications, such as TVs, computers, cars, elevators and copy machines. Few of the most powerful magnets in the world exist in MRI machines. Resembling a doughnut, an MRI electromagnet scans patients to create pictures doctors can evaluate.

Physics is a subject that has a lot of identical aspects. The primary and most important chapters of physics are based on practical knowledge and the day-to-day occurrences of our lives. The multiple topics, such as centripetal force, centrifugal force, speed of light, etc., hold a lot of importance in the students’ curriculum for sure. 

The various equations, such as finding the wavelength, displacement, or speed of light, or finding the value of C, are little complicated equations that lead to brainstorming the students. Detecting them is a tricky thing and needs a lot of hard work to get identified, and that is why having appropriate tools to identify them is very crucial. 

 

Importance of Speed of Light Chapter in Physics:

The speed of light is a fundamental concept in Physics as many things and equations resolve around the same and cannot be completed without detecting it in the first place. Some other important factors that make the speed of light chapter important and separate can be listed as follows-

 

The Time Difference Can be Significantly Reduced with Speed of Light: 

The time in which light travels in space is definitely in microseconds. For the same reason, the people on the planets lack behind a lot. To make sure this difference gets significantly reduced, many physicists and scientists are trying hard to find the most effective time-reducing solution and lower the gap between the time of the two planes. 

Therefore, with the help of light speed, Physicists can detect the time equations in a much effective way and find appropriate solutions for the respective problems. 

 

Helps in Detecting the Masses of the Objects:

Light has a very negligible mass, and that is why it can travel at such a considerable speed. By detecting or tracing this time-span and mass, the other objects can also be increased or reduced in their masses. 

For the same reason, proper knowledge about the speed of light can help people detect the masses of various other objects very quickly and without consuming much time. 

 

Consistency in Objects Can be Traced Easily:

Speed of light is something that is always constant and does not get affected because of any medium. This can be appropriately studied and implemented on the other objects as well, and for the same reason, the importance of speed of light is massive in its place or way for sure. 

All the above points describe the importance of the speed of light in the Physics subject to a great extent. For all the above reasons, the speed of light should be chosen by the students in the first place so that they can get fully relieved about Physics in the future.

Conclusion: 

Speed of Light’s importance is tremendous in Physics, and almost all the things related to Physics rotate around this individual concept. For the same reason, all the concepts and equations associated with the value of light’s speed should be appropriately considered by the students in the first place itself. This will avoid future stress and confusion for them and make Physics enjoyable and scoring for them. 

The velocity of light value and the value of C in physics is largely, and the student who understands this properly can freely qualify for any examination or test related to Physics coming in their way. Therefore, attaining perfection in detecting the value of c and knowing how to calculate the speed of light remains the most crucial aspect for the students for sure. 

Velocity in physics is defined as a vector measurement of the direction and rate of the motion. To be specific, the velocity of an object can also be defined as the rate of change in the object’s position corresponding to a frame of reference and time. In simple words, the term velocity gives us an idea of the speed at which an object is moving in a particular direction. It is what tells how slow or fast something is moving. Let’s take an example where two objects are moving. Identifying which of the two objects is moving faster than the other one is easy if they both are moving in the same direction. However, determining the faster object is quite difficult if the two are travelling in opposite directions. Considering such difficulties and thus eliminating them, our scientists came up with the concept of velocity to help the observers in identifying the faster or slower objects with ease. Here, we will be going to discuss this concept in detail. 

What is Velocity?

Velocity is a vector measurement of the rate of motion of an object and the direction in which it is moving. Hence, to determine the velocity as per this definition, we should be familiar with both the magnitude and direction. For instance, if an object travels towards the west at 5 meters per second (m/s), then its velocity will be 5 m/s to the west. A simple formula given below is the most common and easiest way to calculate velocity.  

r = d / t

where,

r is the rate (sometimes denoted as v, representing velocity)

d is the distance the object moved 

t is the time the object took to complete the movement

Units of Velocity

Although the SI unit for velocity is m/s (meter per second), it can be expressed in any unit of d/t (distance per time). Some of the units in which one can express velocity is miles per hour (mph), kilometres per second (km/s), and kilometres per hour (kph).

Initial and Final Velocity

Initial velocity is the speed (along with direction) of the object with which it starts moving. On the other side, the final velocity is the speed (along with direction) of the same moving object once it has reached its final position. 

How to Find the Initial Velocity?

The initial velocity (vi) is the velocity of the object before a change due to acceleration. Hence, it can be calculated by using the below formula:

vi = vf – at

where, 

vi = initial velocity (m/s)

vf = final velocity (m/s)

a = acceleration (m/s²)

t = time between the start and end of the acceleration (s)

How to Find the Final Velocity?

The final velocity of an object is equal to its initial velocity plus acceleration multiplied by the time it travelled, and can be given as:

v = u + aΔt

where, 

v = final velocity

u = initial velocity

a = acceleration 

t = time 

As the equation shows; for a given object, you can calculate its final velocity by adding its initial velocity to the acceleration due to force multiplied by the time for which the force applied to it. The delta (Δ) in front of the time (t) displays the change in time, which can be written as tv − tu. Here, tv – tu is the time elapsed from u to v.

Speed and Velocity

Most of us often get confused by the terms speed and velocity, as the concepts of both of these terms revolve around how fast something is moving. Well, although the concepts are a bit similar, these terms are quite different from each other. The main difference between speed and velocity is that speed gives an idea of how fast the body is moving, whereas velocity not only gives the idea of the body’s speed but also tells the direction in which it is moving. Speed is related to distance travelled, whereas velocity is to displacement. Average velocity, which is the total displacement by total time, is always either less than or equal to the average speed. It is so because the displacement can never be more than the distance travelled, whereas the distance travelled can be more than the displacement.    

Difference between Speed and Velocity

The basic difference between speed and velocity is that the former has only magnitude, while velocity has both magnitude and direction. It means the velocity is the speed with direction. 

Other Detailed Differences between Speed and Velocity are as Follows:

Speed is the quantitative measure of how fast a body is moving, whereas velocity measures not just the speed at which the body is moving but also the direction in which it is moving. In other words, speed determines only how fast something is travelling, while velocity determines how fast something is travelling, along with the direction of its movement.  

As the speed emphasizes only the magnitude, it is termed as a scalar quantity. On the other hand, the velocity is a vector quantity as it focuses on both the magnitude and direction. 

Speed is defined as the rate of change of distance, whereas velocity refers to the rate of change of displacement.

The average speed of a moving body can never be zero or negative. But, the velocity of a moving body can undoubtedly be zero.

Speed is distance/ unit time. On the other side, velocity is displacement/ unit time.