Category: Physics Notes PPT

When a stationary car starts suddenly, we get pushed up backward, and when brakes are applied, we get pushed forward against our seat, or when our car takes a sharp right turn, we get pushed towards the left. We experience these situations because our car is accelerating.

Simply when there is a change in Velocity, there will be Acceleration. Let’s understand the concept of Acceleration with illustrative examples.

Let’s suppose I have a car moving with a constant Velocity of 90 kmph along a straight line. I can see a helicopter flying at roughly a speed of 20,000 kmph. If I were to ask you that in these two cases, where do you find the Acceleration? Your answer will be surely no because both are moving at a constant pace, so no Acceleration in both cases. 

Now, if I ask you that Acceleration is equal to high speed. What will be your answer? You may say yes, but that’s not true for sure.  Want to know why?  It’s because Acceleration is the rate of change of Velocity. Now, let’s understand the Acceleration formula.

 

General Formula of Acceleration

We already know that Velocity is a speed with direction; therefore, it is a vector quantity. The Acceleration ‘a’ is given as:

      [ a  = frac{text{Change in Velocity}}{text{Time Taken}}]

This formula states that the rate of change in Velocity is the Acceleration, or if the Velocity of an object changes from its initial value ‘u’ to the final value ‘v’, then the expression can be simply written as:

                         [a =  frac{(v – u)}{t}]        

 

Acceleration Formula in Physics 

In Physics , Acceleration is described as the rate of change of Velocity of an object, irrespective of whether it speeds up or slows down. If it speeds up, Acceleration is taken as positive and if it slows down, the Acceleration is negative. It is caused by the net unbalanced force acting on the object, as per Newton’s Second Law. Acceleration is a vector quantity as it describes the time rate of change of Velocity, which is a vector quantity. Acceleration is denoted by a. Its SI unit is [frac{m}{s^{2}}] and dimensions are [[M^{0}L^{1}T^{–2}]].

If [v_{0}, v_{t}] and t represents the initial Velocity, final Velocity and the time taken for the change in Velocity, then, the Acceleration is given by:

[overrightarrow{a} = frac{overrightarrow{v_t} – overrightarrow{v_0}}{t}]

In one dimensional motion, we can use;

[a = frac{v_t – v_0}{t}]

 

Acceleration Formula

If [overrightarrow{r} ]represents displacement vector and [overrightarrow{v} = frac{overrightarrow{text{d}r}}{text{d}t}] represents the velocity, then;

Acceleration:  [overrightarrow{a} = frac{overrightarrow{text{d}v}}{text{d}t} = frac{overrightarrow{text{d}^{2}v}}{text{d}^{2}t}]

In one dimensional motion, where x is the displacement, and [v = frac{text{d}r}{text{d}t}] is the Velocity, then;

[a = frac{text{d}{v}}{text{d}t} = frac{text{d}^{2}x}{text{d}^{2}t}]

Example 1:

A car starts from rest and achieves a speed of 54 [frac{km}{h}] in 3 seconds. Find its Acceleration?

Solution:  [v_0] = 0, [v_t] = 54 [frac{km}{h}] = 15 [frac{m}{s}], t = 3s, a = ?

Acceleration:  

[a = frac{v_t – v_0}{t} = frac{15 – 0}{3} = 5 frac{m}{s^{2}}] 

Example 2:

A body moves along the x- axis according to the relation [x = 1 – 2 t + 3t^{2}], where x is in meters and t is in seconds. Find the Acceleration of the body when t = 3 s

Solution:

We have: [x = 1 – 2 t + 3t^{2}]

then; Velocity [v = frac{text{d}x}{text{d}t} = -2 + 6t ]

Acceleration:  [v = frac{text{d}v}{text{d}t} =  6  frac{m}{s^{2}}].

(We see that the Acceleration is constant here. Therefore, at t = 3s also, its value is 6  [frac{m}{s^{2}}]).

 

Solved Questions Using Acceleration Formula:

1. What will be the Acceleration of a Car if it Slows from 90 [frac{km}{h}] to a Stop in 10 sec? 

Here, u = 90 [frac{km}{h}] = [ frac{90 times 5}{18} = 25 frac{m}{s^{2}} ] because initially it was moving at a speed of 90 kmph then reached zero.

Final Velocity ‘v’ = 0 kmph, and t  = 10 seconds

Now, applying the formula here:

[a  = frac{(0 – 25)}{10}  = (-) 2.5 frac{m}{s^{2}} ]

2. A Girl Starts her Motion in a Straight Line at a Velocity of 30 [frac{m}{s}], her Velocity is Changing at a Constant Rate. If She Stops after 60 s, What is her Acceleration?

Answer: Here, the initial Velocity of a girl was 30 [frac{m}{s}] and stops, so her final Velocity will become 0 m/s. Now, the deceleration or retardation occurs, which is just the opposite of Acceleration and it can be determined as:

                  [  a  = frac{(0 – 30)}{60} = (-) 0.5 frac{m}{s^{2}} ]

Question 3: A Car Moves in a Circular Track with a Constant Velocity; will it Experience Acceleration?

Answer: Here, the speed is constant; however, the direction is continuously varying, which means the Velocity is also varying. It states that the car will experience Acceleration.

 

How to prepare for a test on Acceleration using

• You can log onto and then go through the study material that’s present

• You can click on Acceleration Formula with examples and solved problem

• After going through this study matter, the concepts will get much clearer

• You can also make notes of the above by writing down the important points

• Carefully observe the solved examples 

• The matter will have ensured that you are preparing well for the exams

 

Why choose ?

is a top e-learning platform that only keeps the best study material on its website. It is extremely dependable since all students bank on it before they sit down for revisions or tests. The study material on it is free of cost and can be downloaded and then gone through in the offline mode as well. You should choose if you need to be smartly prepped up before your tests and learn all the complex concepts.

When the heat is absorbed by a body, its temperature increases, and when the body discharges or loses heat, its temperature falls. The heat capacity is the heat needed for raising the temperature of an object by a calculation of one degree. It can also be calculated as a ratio of the amount of heat energy that is given to the object for the resulting increase in the temperature. The expression for the heat capacity is [c = frac{{Delta Q}}{{Delta T}}].

 

Here, ΔQ is the amount of heat that is transferred, ΔT is the increase in temperature. 

There is an equal fall in temperature when the body loses the same quantity of heat. In SI units, the heat capacity can be expressed by joule per kelvin, (J/K). In the heat capacity, the body mass can have any value, which is not specified, such as unit mass etc.

An Example of the Heat Capacity

When 6400 J of heat is supplied to the body and it raises its temperature by approximately 100 degrees, then what is its heat capacity?

Solution: [Delta Q = 6400,J,,,,Delta T = 100^circ ,,,,c = ?]

Heat capacity; c [c = frac{{Delta Q}}{{Delta T}} = frac{{6400}}{{100}} = 64,J/K,,].

Practice Questions

If you want to check out the different practice questions and their solutions, you can refer to the notes on heat capacity formulas. Here you will find a wide comprehensive explanation of the concept, a wide range of examples, and an array of practice questions with solutions including multi choice questions. The solved practice questions can help you gain an understanding of the different types of questions that are likely to be asked in the exams and the process of solving them. Referring to these notes can help you prepare thoroughly for your exams.

is a top destination for learning material and resources for students of different branches, fields, domains, and subjects. Here you get a comprehensive list of different subjects and chapters plus useful tutorials as well as notes that are important for your exam preparation. The solution sets for different chapters, solved question paper, sample question and answers, formulae, tutorials, and notes provided by are amongst the finest learning material that you can find online.

You can also download the app for quick access to some of the most reliable and high quality learning material for your exams. Most of these resources are available to download for free, which is why continues to be one of the most preferred destinations for a lot of students. 

Torque is a type of measurement that can be applicable for an object which rotates about an axis. You all know that force is the only factor in linear kinematics that causes acceleration of a body. 

Just like force, Torque is involved with an angular acceleration of the body. The axis of rotation is a point where a body begins its rotation. In this article, we will read in brief regarding the torque formula physics. Physics has a simple explanation of the torque that is the tendency of a force that promotes twisting. 

Torque Calculator

Physicists have developed a simple path that leads to a torque calculation formula.

(Image to be added soon)

To do so, we need to find the lever arm. After that, just multiply it with the applied force. Till now, you know that torque can be produced on two factors such as the magnitude of the force and normal distance (perpendicular distance) between the point (torque is applicable here) about which torque is calculated.

So, the Torque Force Formula is equal to  τ = F.r. sin⁡θ

Here, τ = Torque

F = Force

θ = Angle between the force and point 

r = Total Length of the arm of the lever

Engine Torque Formula

The unit used for the measurement of torque is Newton-meter (N-m). We have discussed the equation that helps us to calculate the torque. Well, the above relation is based on the vector product of position vector and force.

τ = F x r 

This is the torque formula that we use to calculate for the engine. 

Torque in a Car

As we know, the expression that defines the twisting force or rotational force is known as torque. Engines provide torque to the axle that is present inside the car. The engine is responsible for producing the rotational force. This torque is considered as the strength of a vehicle.

If the engine is capable enough to provide maximum torque, then the car will give you maximum output. All sports cars are using these types of engines where torque is maximum. The engine will give a boost to the car within o to 60 seconds. Also, heavy vehicles such as trucks, tractors, and others are using these types of engines.

Maximum Torque Formula

This is the formula that explains the maximum Torque in a three-phase motor

 Tmax= [k.frac{E_{2}^{2}}{2X_{2}}]

Conclusion

Torque plays a crucial role in generating power from the engine of a car. Torque is a value that represents the capacity of an engine to handle or generate maximum power to rotate the axle. An engine’s power output is measurable with RPM. This is only possible with the maximum generated torque.

The amount of fluid (water flow rate formula) moving through any position through a region during a period of time is known as the volume flow rate Q. The volume flow rate formula can be written in symbols as:

Q = [frac{V}{T}]

where V denotes volume and t denotes time. The SI unit for the flow rate is m/s, although there are many other units for Q in general use. A sleeping adult’s pulse, for example, pumps blood at a rate of 5.00 litres per minute. A litre (L) is equal to 1/1000 of a cubic meter or 1000 cubic centimetres. Flow rate and velocity are two physical quantities that are related but not identical. Consider the flow velocity of a river to help you understand the difference. The river’s flow rate increases as the velocity of the stream increases. However, the scale of the river has an effect on the flow rate.

[]

Q = A[bar{v}] is the same relationship between flow rate Q and velocity [bar{v}], where [bar{v}] is the average velocity, and A is the cross-sectional area.

The method for obtaining this relationship is seen in the above figure. The volume V = Ad of the shaded cylinder flows past the point P in time t. 

The following is obtained by multiplying both sides of this relationship by t:

[frac{V}{t}] = [frac{Ad}{t}]

We know that Q = [frac{V}{T}] and the average speed is denoted by [bar{v}] = [frac{d}{t}],

Therefore, 

Q = A[bar{v}]

Mass Flow Rate Formula

The conservation of mass is a basic physics principle. The sum of mass in certain problem domains remains stable — mass is neither produced nor lost. The mass of every object is equal to the volume of the object multiplied by its density. The density, volume, and shape of a fluid (a liquid or a gas) will all vary with time within the domain. Furthermore, the mass will shift inside the domain. A gas flow into a constricted tube is depicted in the diagram. There is no mass deposition or destruction in the tunnel; the same volume of mass reaches and exits the tube. The same volume of mass flows through the tube in every plane perpendicular to the middle line. The mass flow rate formula is the volume of mass that passes through a plane. The principle of mass conservation (continuity) states that the mass flow rate equation into a conduit is constant. The mass flow rate can be calculated using the flow conditions.

The mass flow rate equation formula is given by,

[dot{m}] = [frac{dm}{dt}]

IV Flow Rate Formula

The drop factor is used to measure the drops per minute. The IV flow rate (drip rate) is calculated using the following formula: total volume (in mL) divided by time (in min), multiplied by the drop factor (in gtts/mL), equals IV flow rate in gtts/min.

Air Flow Rate Formula

Using the continuity equation for gases, you can measure air flow patterns in various parts of a pipe or hose system. Both liquids and gases are considered fluids. The mass of air entering a straight and sealed pipe system equals the mass of air exiting the pipe system,  as per the continuity equation. 

Calculation of Flow Rate Using Pressure

How to Calculate Flow Rate from Pressure?

We use Bernoulli’s theorem to calculate the differential pressure measurement for different flows.

To begin, we must first understand fluid dynamics, or more specifically, Bernouilli’s concepts – the physics behind the differential pressure flow meter. Bernoulli was a Swiss mathematician who studied energy conservation in the 1700s. In a nutshell, the theory named after him states that the number of all energies – static, potential, and kinetic – in a fluid flowing through a pipe stays constant within the pipe.

The sum of all these energies upstream equals the energies downstream for a differential pressure meter. Static energy is represented by pressure, potential energy by height, and kinetic energy by velocity.

Solved Examples

1. What is a material’s mass flow rate if 20 ml of it is obtained in 20 seconds? The substance has a density of 0.5 gm/ml.

1. 0.5

2. 0.1

3. 0.2

4. 1

Solution:

We know, Mass flow rate= Mass/Time

Mass= Volume x Density

Mass=20 x 0.5= 10

Mass flow rate= 10/20=0.5

Answer: a) 0.5

2. 100 grams of liquid is obtained in 10 seconds at what mass flow rate of the liquid passing through a pipe?

Solution: 

Let us convert 100 grams in terms of kilograms, we get,

Mass = 0.1kg and the time is 10 seconds, 

Therefore, Mass Flow Rate = [frac{0.1}{10}] = 0.01 Kg/s 

Energy consumption can be simply said to be the use of a specific amount of energy or power output. This can be the energy consumption related to the consumption of electrical power generated by power plants or the energy derived from food in the case of biological living organisms. Although both are energy consumption and both of them have their unique formulas, here we are primarily going to discuss the energy consumption regarding the consumption of an electrical output or the energy generated by a power plant. 

As mentioned, energy consumption is the use of the power of the energy of any system by making use of the supplied power. Energy is measured in terms of Joules as it is the standard Unit of Energy measurement, and so the energy consumption is typically observed in Gigajoules per year which is kilograms of the oil equivalent per year and in Watts. Hence, the energy calculation formula or the formula of energy consumed for determining energy consumption is obtained by calculating the number of power units consumed over a given period. 

 

Energy Consumption Formula

As mentioned above in the introduction, energy consumption is measured by multiplying the number of power units consumed within the period over which it has been consumed. Hence, the energy consumption formula or the power consumption formula is given as below:

E = P*(t/1000); where E = energy measured in Joules or kilowatt-hours (kWh), P = power units in watts,  and t = time over which the power or energy was consumed.   

Thus, whenever someone asks you how to calculate power consumption, you can calculate and answer using the above equation. 

Energy consumption can be widely classified based on several factors such as worldwide energy consumption, its impact on the environment, etc. 

Based on the idea of demographic usage, energy consumption can be divided into the following categories:

• Worldwide Energy Supply: The worldwide energy supply is a vast area that is defined based on the factors such as the global production and preparation of the fuel, generation of the electricity using that fuel, the transport of energy and energy consumption. 

• Worldwide Energy Consumption: It is the overall energy consumed of the total available output of the energy produced which is huge in number. This is done by using the power consumption formula and calculating the total power consumption at different levels of demographics. 

• Domestic Energy Consumption: Domestic energy consumption is defined as the total amount of energy consumed by a given household or for household work. Usually, the power consumption of a household activity calculated using the above-given power consumption formula may be small but when multiplied by the number of households of the population in a given demographic the number becomes significant. 

• Electric Energy Consumption: This classification is defined based specifically on the consumption of electrical energy consumed. It does not include the amount of mechanical energy that is used to perform work. Here, the energy consumed formula or power consumed formula can be applied by taking the values of power units based on the meter readings installed at various places such as household or industrial locations. 

Energy consumption has been central to the development of human civilizations. White’s Law named after Leslie white and published in 1943 states that with most of the other factors remaining constant, “culture evolves as the amount of energy harnessed per capacity per year is increased or as the efficiency of the instrumental means of putting the energy to work is released”.

There are widespread effects of energy consumption worldwide. The impact of the energy industry on the environment has been huge and mostly negative. The ever-increasing amounts of energy being produced and the increasing rate at which the energy is consumed has resulted in the generation of harmful factors that have immensely contributed to the rise of Earth’s temperature significantly within a few years. Because of coal and petroleum products being used more and more until recently to produce and fulfil the immense needs of energy, there has been a continuous release of greenhouse gases such as carbon dioxide and different oxides of nitrogen that have contributed significantly to the greenhouse effect. Not only the production but the consumption of energy ranging from household activities to industrial activities have generated and released immense amounts of heat energy into the atmosphere. Therefore, unchecked production from non-renewable sources and the unchecked consumption of energy has resulted in global warming which needs to be taken seriously and taken care of. 

 

Energy consumption

Energy consumption defines the use of energy. It is the use of energy specifically for a definite amount. This is related to the energy consumption of electrical power generated through power plants or energy used by any living creature. Both types of consumption of energy vary from each other. Joules is the term used to scale energy as a standard unit of measurement, hence the energy is generally observed as gigajoules per year. The formula to calculate energy is derived for the calculation of consumed energy in a specific period. 

The formula for Energy Consumption

The formula of energy is used to calculate the use of energy for a given period. The consumption of energy is measured by multiplying the number of power units consumed in a given period. The formula for consumption of energy is given below-

E = P*(t/100)

In this formula, E refers to the measured Joules or kilowatt per hour (kWh).

P refers to power used per unit in watts.

t refers to the time over which the power is consumed.

Hence, to calculate the consumption of energy one can use this formula.

The consumption of energy is classified into several factors, some of them as discussed below –

1. Worldwide energy supply – as the name specifies, the world is a large area to discover. Hence, the supply of energy is also vast that has to be defined based on the factors like global preparation and production of fuel generation for electricity, energy consumption, and the energy used for transportation.

2. World energy consumption – the energy consumed as compared to the energy available the use of all over the world. This energy is calculated by using the energy consumption formula i.e. E = P*(t/100) at different levels of demographics.

3. Domestic energy consumption – domestic energy consumption is the consumption of energy used by the household or by the household work. Generally, the formula of energy consumption is used to calculate the domestic energy consumption by multiplying it with the number of households of the population given demographics.  

4. Electric energy consumption – in this classification, specifically the consumption of energy in the form of electricity is considered. It does not include any other type of energy that is used to perform work. Also, the formula for the energy consumption can be used here by taking the value of power units based on the meter readings.  

 

Conclusion

To curb and control the harmful effects of energy consumption, energy conservation is necessary. Energy conservation is the practice of decreasing the total quantity of energy or using the energy more efficiently and avoiding any wastage of energy. This not only addresses the challenge of wastage of energy resulting inequitable distribution of energy amongst the people but also in providing a cap on the energy requirements and the energy generated by the industries so that there is less release of greenhouse gases into the atmosphere thus, in turn, helping the environment and the planet from not going to the verge of drastic environmental changes and extinction of most of the species.

Heat is one of the significant components of phase change that is associated with work and energy. Heat transfer is defined as the process of flow of heat from an object at a higher temperature to an object at a lower temperature. The heat flow equation covers the heat transfer mechanism, such as the conduction equation, convection formula, thermal radiation, and evaporate cooling.

On this page, we will understand the heat transfer formula, the rate of heat transfer formula, and the type of heat flow equation in detail.

Heat Flow Equation

The formula heat energy describes the amount of heat transferred from one object to another.

So, the amount of heat transferred from one object to another is determined by the following heat transfer formula:

                 Q  =  mcΔT

Here,

Q is the amount of heat added to the system

c  =  Specific heat capacity of the system

At constant Volume, c becomes cV

Similarly, at constant pressure, c becomes cP

Besides this, 

The mass of the system is “m,” and ΔT is the temperature difference, measured in K.

The transfer of heat occurs through the following three different processes:

Now, let’s understand the formula for the types of heat transfer:

Conduction Formula

Heat conduction is the transmission of internal thermal energy as a result of the collisions of microscopic particles and the motion of electrons within a body.

The conduction equation is given by:

                           q   =  – k ▽T

Here,

q  =   Local heat flux density 

– k   = material’s conductivity, and

▽T = temperature gradient

Now, talking about the heat flux formula, it is given by:

Фq  =  – k [frac{dT(x)}{dx}]

Here,

Фq  =  heat flux = the heat divided by the area = [frac{Q}{A}] 

Thermal conductivity is k, and T is the temperature

The SI unit of heat flux is W/m[^{2}] or Watt per meter square.      

Convection Formula

The convection formula is:

                    Q  =  h A ΔT 

Here,

Q = the rate of heat transfer      

h = convection heat transfer coefficient

A = the exposed surface area, and            

ΔT = the difference in temperature 

The temperature difference is between a solid surface and surrounding fluid

For the convection equation unit, we have the following heat transfer coefficient formula: 

                      h = [frac{Q}{Delta T}]

Therefore, the SI unit of convection coefficient is W/(m[^{2}]K).

Rate of Heat Transfer Formula

The rate of heat transfer formula is:

[frac{Q}{t}] = [frac{kA(T_{2} – T_{1})}{d}]

Here,

[frac{Q}{t}] = rate of heat transfer in watts per second (W/s) or kilocalories per second (Kg/s)

k = a thermal conductivity of the material

(T[_{2}] – T[_{1}]) = a temperature difference across the slab

d = thickness of the slab, and

A = surface area of the slab

Thermal Conductivity Equation

The thermal conductivity equation is:

                          Q = [frac{Qd}{A Delta T}]

Here,

k = thermal conductivity, measured in W/m.K

Q = amount of heat transfer, measured in Joules/second or Watts

d = distance between the two isothermal planes

A = surface area in square meters    

ΔT = the temperature difference

Conclusion

The heat generated by the movement of particles in the system. Heat transfer is a process of the exchange of heat from a high-temperature body to a low-temperature body.