Uniform Circular Motion: An Introduction Quiz

Test your understanding of motion around a circle at constant speed. This medium-difficulty quiz reviews period, frequency, angular velocity, and how linear speed relates to rotation.

Remember: constant speed does not mean constant velocity, because the direction of motion changes continuously around the circle.

Q1. Which description best defines uniform circular motion?

Motion along a circular path at constant speed

Motion along a straight path at constant speed

Motion along a circular path with steadily increasing speed

Motion along any path with constant velocity

Uniform circular motion is motion along a circular path while the magnitude of velocity, or speed, remains constant.

Q2. In uniform circular motion, what happens to the angle swept out during equal time intervals?

It is equal in each interval

It steadily decreases

It is zero in every interval

It varies randomly

Uniform circular motion covers equal angles in equal intervals of time, giving the motion a regular rotational rhythm.

Q3. What does the period of a circular motion describe?

The time taken for one complete revolution

The number of revolutions completed per second

The distance from the centre to the path

The angle swept out in one second

The period, ##T##, is the time required for one complete revolution.

Q4. A rotating object completes ##5## revolutions in ##10## seconds. What is its frequency?

##0.5\ \text{Hz}##

##2\ \text{Hz}##

##5\ \text{Hz}##

##50\ \text{Hz}##

Frequency is the number of revolutions per unit time, so ##f=\dfrac{5}{10}=0.5\ \text{Hz}##.

Q5. An object takes ##4\ \text{s}## to complete one revolution. What is its frequency?

##0.25\ \text{Hz}##

##2\ \text{Hz}##

##4\ \text{Hz}##

##8\ \text{Hz}##

Frequency and period are reciprocals: ##f=\dfrac{1}{T}=\dfrac{1}{4}=0.25\ \text{Hz}##.

Q6. A rotor makes ##2## complete revolutions each second. What is its period?

##0.5\ \text{s}##

##2\ \text{s}##

##4\ \text{s}##

##\pi\ \text{s}##

The period is the reciprocal of the frequency, so ##T=\dfrac{1}{f}=\dfrac{1}{2}=0.5\ \text{s}##.

Q7. Which expression gives the angular velocity for a body completing one revolution in period ##T##?

##\omega=\dfrac{2\pi}{T}##

##\omega=\dfrac{T}{2\pi}##

##\omega=2\pi T##

##\omega=\dfrac{1}{2\pi T}##

One revolution corresponds to ##2\pi## radians, so the angle covered per unit time is ##\omega=\dfrac{2\pi}{T}##.

Q8. An object completes one revolution in ##4\ \text{s}##. What is its angular velocity?

##\dfrac{\pi}{2}\ \text{rad/s}##

##2\pi\ \text{rad/s}##

##4\pi\ \text{rad/s}##

##\dfrac{1}{4}\ \text{rad/s}##

Using ##\omega=\dfrac{2\pi}{T}## gives ##\omega=\dfrac{2\pi}{4}=\dfrac{\pi}{2}\ \text{rad/s}##.

Q9. Which is the standard unit of angular velocity when the angle is measured in radians?

##\text{rad/s}##

##\text{m/s}##

##\text{s}##

##\text{Hz}##

Angular velocity measures angular displacement per unit time, so its unit is radians per second, ##\text{rad/s}##.

Q10. A point on a circle of radius ##2\ \text{m}## has angular speed ##3\ \text{rad/s}##. What is its linear speed?

##6\ \text{m/s}##

##1.5\ \text{m/s}##

##5\ \text{m/s}##

##12\ \text{m/s}##

Linear speed and angular speed are related by ##v=r\omega##. Thus ##v=(2)(3)=6\ \text{m/s}##.

Q11. A particle moves on a circle of radius ##2\ \text{m}## through an angle of ##1.5\ \text{rad}##. What arc length does it travel?

##3\ \text{m}##

##0.75\ \text{m}##

##1.5\ \text{m}##

##4\ \text{m}##

For an angle in radians, the arc length is ##s=r\theta##. Therefore, ##s=(2)(1.5)=3\ \text{m}##.

Q12. What angle in radians corresponds to a quarter of a complete revolution?

##\dfrac{\pi}{2}##

##\pi##

##2\pi##

##\dfrac{\pi}{4}##

A full revolution is ##2\pi## radians. One quarter of that is ##\dfrac{2\pi}{4}=\dfrac{\pi}{2}## radians.

Q13. Why is velocity not constant in uniform circular motion, even though speed is constant?

The direction of velocity changes continuously

The object's mass changes continuously

The object stops at each point on the circle

The radius must increase continuously

Velocity includes both speed and direction. In circular motion, the direction changes continuously even when the speed stays the same.

Q14. At a particular point on a circular path, which way does the instantaneous velocity point?

Tangent to the circle at that point

Directly toward the centre

Directly away from the centre

Along the circumference toward every point at once

The instantaneous velocity is tangent to the path. For a circle, this tangent is perpendicular to the radius at that point.

Q15. At any point on a circular path, how is the instantaneous velocity direction oriented relative to the radius?

Perpendicular to the radius

Parallel to the radius

At an angle of ##45^\circ## to the radius

In the same direction as the radius

The velocity is tangent to the circular path, and the tangent is perpendicular to the radius at the point of contact.

Q16. Two positions on a circular path are separated by a quarter revolution. What is the angle between their velocity directions?

##90^\circ##

##45^\circ##

##180^\circ##

##360^\circ##

The velocity directions are tangent to the circle at each position. A quarter revolution separates those tangents by ##90^\circ##.

Q17. In the idealized description used in this lesson, which object is an example of uniform circular motion?

A clock hand rotating steadily

A ball rolling down a slope and speeding up

A car braking along a straight road

A stone falling vertically

A clock hand rotating steadily traces a circular path at constant speed in the idealized example of uniform circular motion.

Q18. A turbine blade tip moves in a circle of radius ##0.5\ \text{m}## and completes one revolution in ##2\ \text{s}##. What is its linear speed?

##\dfrac{\pi}{2}\ \text{m/s}##

##\pi\ \text{m/s}##

##2\pi\ \text{m/s}##

##\dfrac{1}{2}\ \text{m/s}##

The angular speed is ##\omega=\dfrac{2\pi}{T}=\pi\ \text{rad/s}##. Then ##v=r\omega=(0.5)(\pi)=\dfrac{\pi}{2}\ \text{m/s}##.

Q19. An object has angular velocity ##3\ \text{rad/s}## for ##2\ \text{s}##. How much angle does it sweep out?

##6\ \text{rad}##

##1.5\ \text{rad}##

##5\ \text{rad}##

##12\ \text{rad}##

With constant angular velocity, angular displacement is ##\theta=\omega t##. Thus ##\theta=(3)(2)=6\ \text{rad}##.

Q20. Two objects move with the same angular speed, but the second follows a circle with twice the radius of the first. How do their linear speeds compare?

The second object's linear speed is twice the first's

Their linear speeds are equal

The second object's linear speed is half the first's

The second object's linear speed is four times the first's

Since ##v=r\omega##, keeping angular speed fixed makes linear speed proportional to radius. Doubling the radius doubles the linear speed.