## Questions and Answers

What does the period of rotation represent in uniform circular motion?

Time taken for an object to complete one full revolution around an axis

What does the tangential velocity represent in uniform circular motion?

The projected velocity along the tangent of the circle

Which force is responsible for producing the centripetal acceleration in uniform circular motion?

Centripetal force

What remains constant in uniform circular motion?

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In uniform circular motion, what does angular velocity measure?

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What does centripetal acceleration point towards in uniform circular motion?

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In uniform circular motion, the object experiences a force directed towards the center of the circle. What is this force called?

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What is the formula for centripetal acceleration in uniform circular motion?

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What is the relationship between the centripetal force and the mass of an object in uniform circular motion?

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Which type of acceleration always points towards the center of the circle in uniform circular motion?

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What does tangential velocity refer to in uniform circular motion?

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What is the formula for centripetal force in uniform circular motion?

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## Study Notes

## Uniform Circular Motion

Uniform circular motion is a type of motion where an object moves in a circular path with a constant speed. In contrast to uniform rectilinear motion, where the direction remains constant, uniform circular motion involves a constant speed but a continuously changing direction. This motion occurs when an object experiences a centripetal force, which pulls it towards the center of the circle.

### Centripetal Force

According to Newton's laws of motion, an object in uniform circular motion requires a net external force directed towards the center of the circle. This force is known as the **centripetal force**. The magnitude of the centripetal force is directly proportional to the mass of the object and the square of its speed:

[ F_\text{c} = \frac{mv^2}{r} ]

where ( F_\text{c} ) is the centripetal force, ( m ) is the mass of the object, ( v ) is its speed, and ( r ) is the radius of the circular path.

### Centripetal Acceleration

The acceleration in uniform circular motion acts towards the center of the circle and is known as **centripetal acceleration**, abbreviated as ( a_\text{c} ). Its magnitude is given by:

[ a_\text{c} = \frac{v^2}{r} ]

where ( v ) is the speed of the object and ( r ) is the radius of the circular path.

### Tangential Velocity

As an object moves in a circle, its velocity constantly changes direction but maintains a constant magnitude. The **tangential velocity** (( v_{\text{tan}} )) is the projection of the velocity vector onto the tangent of the circle.

### Period of Rotation

The **period of rotation** is the time taken for an object to complete one full revolution around an axis. In uniform circular motion, the period of rotation is constant and depends on factors such as the size of the circle and the speed of the object.

### Angular Velocity

**Angular velocity** (( \omega )) is the measure of how fast an object rotates about an axis. It is the ratio of the angle covered to the time taken to cover that angle. In uniform circular motion, the angular velocity is constant.

### Summary

Uniform circular motion is characterized by a constant speed and continually varying direction. It requires a centripetal force, which produces a centripetal acceleration pointing towards the center of the circle. Tangential velocity describes the projected velocity along the tangent of the circle. The period of rotation and angular velocity remain constant in uniform circular motion.

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