## Key Concepts

- Uniform circular motion
- Timeperiod

**Introduction:**

In this session you are going to read about uniform circular motion and relate radius of the circle formed during circular motion, speed of the object and the time period.

**Explanation:**

**Uniform Circular Motion**

It is the motion of an object traveling at a uniform speed on a circular path.

- It can be uniform with constant speed.

- It can be non-uniform with the change in rate of rotation.

In a uniform circular motion, the speed or the magnitude of the velocity is constant.

Direction of the velocity vector is not constant. Since there is a change in direction, there is acceleration.

**Time period**

Time period in a uniform circular motion is the time required to travel once around the circle, that is to make one complete revolution.

T =

2πrv2πrv

Where, r is the radius of the circle formed,

v is the velocity of the moving object, and

T is the time period of one revolution.

**Examples of uniform circular motion:**

- Motion of artificial satellites around the earth.

2. Motion of electrons around the nucleus in an atom.

3. Motion of blades of a windmill.

d. Motion of the second, minute and hour hand in a watch or a clock.

**Questions and answers**

**Question 1: List a few examples of uniform circular motion from your daily life.**

**Answer:**

A few examples of uniform circular motion from daily life are:

- Satellites orbiting around the earth.

- Revolution of earth around the sun.
- Driving a car on a circular path.
- Giant wheels in an amusement park.

**Question 2: ****What is the time period of motion of a boy in a merry-go-round if the radius of the merry-go-round is 20 m and the speed of the boy around the merry-go-round is 40 m/s. **

**Answer:**

Radius of merry – go – round = 20m

Speed of boy = 40 m/s

According to formula, T =

2πrv2πrv

= 2 × 3.14 ×

20402040

= 3.14 s

**Question 3: ****The wheel of a car has a radius of 0.34 m and is being rotated at 900 revolutions per minute (rpm) on a tire balancing machine. Determine the speed in standard units at which the outer wheel of the car is moving.**

**Answer:**

Answers:

900 revolution in 1 minute

So 1 revolution in

19001900

min =

19001900 × 60

= 0.07 s

∴ ∴

Time period = 0.07 s

Radius = 0.34 m

According to formula, T =

2πrv2πrv

2 × 3.14 × 0.340.072 × 3.14 × 0.340.07

= 30.5 m/s

### Summary

- Uniform circular motion is the motion of an object traveling at a uniform speed on a circular path.
- There is acceleration in uniform circular motion.
- Time period in a uniform circular motion is the time required to travel once around the circle, that is to make one complete revolution.

**T**=2πr/v

- A few of the applications where this is used is:

1. Satellites orbiting around earth.

2. Revolution of earth around sun.

3. Driving a car in a circular path.

4. Giant wheels in an amusement park.

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