Uniform Circular Motion

Uniform Circular Motion

Prepared By: Shah Izat Mir

Objectives

(SLO 5.1 to 5.5)

By the end of the session the CPs will be able to:

• Define angular displacement, angular velocity, angular acceleration, centripetal

acceleration, centripetal force, moment of inertia, angular momentum, and rotational
kinetic energy wit SI Unit and dimensions.

• Discuss the relation between angular and linear displacement, velocity and

acceleration.

• Derive centripetal acceleration when speed is uniform and relate centripetal

acceleration with angular velocity.

• Explain the law of conservation of angular momentum.

• Derive an expression for rotational kinetic energy.

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ANGULAR VELOCITY:

• In simple words, angular velocity is the time rate at which an

object rotates or revolves about an axis. Angular velocity is
represented by the Greek letter omega (ω, sometimes Ω). It is
measured in angle per unit time; hence, the SI unit of angular
velocity is radians per second. The dimensional formula of
angular velocity is [M0 L0 T-1].

• Angular velocity is also known as rotational velocity and

angular frequency vector.

Angular velocity is the vector measure of the
rotation rate, which refers to how fast an object
rotates or revolves relative to another point.

Angular Acceleration:

angular acceleration (α) is the rate of change of

angular velocity with time. Therefore, α = dω/ dt

TASK-1

Think for 2 minutes and write down your response within a
minute for the following two questions.

1. Can an object be accelerated if its speed remains constant?

2. Can an object be accelerated if its velocity remains constant?

Share your answer with your pair with in two minutes.

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Centripetal Acceleration

An object in uniform circular motion is
continuously changing direction, and
therefore is constantly changing velocity

The object must therefore be accelerating.
This is called the centripetal acceleration
and is perpendicular to the direction of the
linear velocity.

Centripetal means it acts towards the
center of the circular path.

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Centripetal Force

A centripetal force is a force that makes a body follow a curved path. The

direction of the centripetal force is always orthogonal to the motion of the body

and towards the fixed point of the instantaneous center of curvature of the path.

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Moment Of Inertia, Angular Momentum,
And Rotational Kinetic Energy

The quantity expressed by the body resisting angular acceleration which is the sum of the
product of the mass of every particle with its square of a distance from the axis of
rotation.

The property of any rotating object given by moment of inertia times angular velocity.

Rotational kinetic energy is the energy an object possesses due to its rotation around an
axis. It depends on the shape, mass and angular velocity.

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TASK-2

• Complete the following chart in your notebook. Time: 10 minutes. Share the

completed table with the CPs in 5 Minutes.

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S.No
Quantity

SI Unit

Dimension

Formula

Scalar/Vector

1 Linear Displacement

2 Angular Displacement

3 Angular Velocity

4 Angular Acceleration

5 moment of Inertia

6 Angular Momentum

7 Angular kinetic Energy

Derive centripetal acceleration when speed is uniform and
relate centripetal acceleration with angular velocity.

D:\OneDrive - Aga Khan Education Service, Pakistan\Desktop\CP_Ch6. Uniform Circular
Motion and Gravitation.pdf

D:\OneDrive - Aga Khan Education Service, Pakistan\Desktop\centripetal acceleration
derivation.mp4

https://www.youtube.com/watch?v=XgkzeUxChKU

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TASK-3

• Explain the law of conservation of

angular momentum.

•

Derive an expression for
rotational kinetic energy.

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• Complete the following tasks within 10

minutes and present for all within 5
minutes by any two CPs. The CPs will be
nominated by the facilitator.

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• D:\OneDrive - Aga Khan Education Service, Pakistan\Desktop\circular_motion_mcq.pdf

THANK YOU

References

• https://byjus.com/physics/conservation-of-

momentum/#:~:text=The%20law%20of%20conservation%20of%20momentum%20states%20that
%20in%20an,neither%20be%20created%20nor%20destroyed.

• https://unacademy.com/content/wp-content/uploads/sites/2/2022/10/Circular-Motion_TEXT.pdf

• https://www.lehman.edu/faculty/anchordoqui/chapter06.pdf

• https://pmt.physicsandmathstutor.com/download/Maths/A-

level/Further/Mechanics/Edexcel/FM2/Cheat-Sheets/Ch.1%20Circular%20Motion.pdf

• https://openstax.org/books/physics/pages/6-2-uniform-circular-motion

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