[Physics Class Notes] on Uniform Circular Motion Pdf for Exam

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.