Free Angular Velocity MCQs with Answers

1. A wheel rotating at 300 revolutions per minute has an angular speed of about

• A. 5 radians per second
• B. 31.4 radians per second
• C. 300 radians per second
• D. 1885 radians per second

Explanation: 300 revolutions per minute is 5 revolutions per second, and each revolution is 2 pi radians, so omega is 5 times 2 pi, which is 31.4 radians per second. Forgetting to convert revolutions into radians leaves the answer as 5, the commonest error here. The value 1885 comes from using minutes rather than seconds.

2. A body moving in a circle at constant speed

• A. has zero acceleration
• B. is accelerating, because the direction of its velocity is continuously changing
• C. has a constant velocity
• D. experiences no net force

Explanation: Velocity is a vector, so changing its direction is a change in velocity even when the magnitude is fixed, and that change per unit time is the centripetal acceleration directed towards the centre. A net force must therefore act, supplied by tension, gravity, friction or the normal force depending on the situation. This is the single most tested idea in circular motion.

3. The so-called centrifugal force experienced by a passenger on a turning bus is

• A. a real force acting outwards on the passenger
• B. the reaction to the passenger's weight
• C. an apparent force arising because the passenger is in a rotating, non inertial frame
• D. always larger than the centripetal force

Explanation: In the ground frame the passenger simply continues in a straight line by inertia while the bus turns beneath them, so no outward force is needed to explain the motion. The outward push is felt only because the observer is accelerating with the bus, which makes it a fictitious or pseudo force. The genuine force in the situation is the inward one supplied by the seat and the floor.

4. The time period T and the angular speed omega of circular motion are related by

• A. T equals omega over 2 pi
• B. T equals 2 pi omega
• C. T equals 2 pi over omega
• D. T equals omega squared

Explanation: One complete revolution covers 2 pi radians, so the time taken is 2 pi divided by the angular speed. A larger omega therefore means a shorter period, which is the inverse relationship the formula expresses. Frequency, being the reciprocal of the period, is omega divided by 2 pi.

5. The moment of inertia of a body depends on

• A. its mass only
• B. its mass and how that mass is distributed about the axis of rotation
• C. its angular speed
• D. the torque applied to it

Explanation: Moment of inertia is the sum of each mass element multiplied by the square of its distance from the axis, so moving mass further out increases it sharply even when the total mass is unchanged. This is why a hollow cylinder has a larger moment of inertia than a solid one of the same mass. It plays the same role in rotation that mass plays in linear motion.

6. A skater spinning with arms outstretched pulls the arms inwards. The result is that

• A. the angular speed increases, because the moment of inertia decreases and angular momentum is conserved
• B. the angular speed decreases
• C. the angular momentum increases
• D. nothing changes

Explanation: With no external torque the angular momentum, the product of moment of inertia and angular speed, stays constant, so reducing the moment of inertia must raise the angular speed. The skater's rotational kinetic energy actually increases, and the extra energy comes from the muscular work done pulling the arms in against the outward tendency. The same principle explains the spin of a collapsing star.

7. The angular momentum of a rotating rigid body is given by

• A. I alpha
• B. I omega
• C. m v r squared
• D. half I omega squared

Explanation: Angular momentum is the moment of inertia multiplied by the angular speed, the rotational analogue of linear momentum mv. The product I alpha is torque, the analogue of force, and half I omega squared is rotational kinetic energy. Keeping these three analogues apart is what most rotational questions actually test.

8. The rotational kinetic energy of a body is

• A. half m v squared
• B. I omega
• C. half I omega squared
• D. I alpha

Explanation: Replacing mass with moment of inertia and linear speed with angular speed in the familiar expression gives half I omega squared. A rolling body has both this and the translational half m v squared, which is why a ball rolling down a slope reaches the bottom more slowly than one that slides without friction. The share of the energy going into rotation depends on the shape of the body.