Arotating object has an angular acceleration of α = 0 rad/s2. which one or more of the following three statements is consistent with a zero angular acceleration?

a. the angular velocity is ω = 0 rad/s at all times.
b. the angular velocity is ω = 10 rad/s at all times.
c. the angular displacement θ has the same value at all times.

A,B and C

Explanation:

Statement A  

At all times, angular velocity is  

Angular acceleration is the rate of change in angular velocity with respect to time.  

Angular velocity and angular acceleration are related by  

Which when re-arranged becomes  

There’s no change in angular velocity anytime when the angular velocity is

The equation can be modified as follows:  

Therefore, the angular acceleration becomes zero hence statement A is valid.  

Statement B  

Angular acceleration is the rate of change in angular velocity with respect to time.  

Angular velocity and angular acceleration are related by  

Which when re-arranged becomes  

There’s no change in angular velocity anytime when the angular velocity is .The final and initial velocities remain the same.  

The equation can be modified as follows:  

Therefore, the angular acceleration becomes zero and statement B is valid  

Statement C  

Angular velocity is defined as the change in the angular position with respect to time.  

Angular velocity and angular displacement are related by  

Which can also be modified as:  

Note that the final position is and initial position is

Modifying the equation to find the angular velocity we obtain  

When the angular displacement has the same value at all times, the equation becomes  

The angular velocity becomes zero.  

Angular acceleration and angular velocity are related by  

The expression above can be rearranged as follows:  

At all times, the angular velocity is hence initial and final velocities remain the same  

We obtain  

Therefore, the angular acceleration becomes zero and statement C is valid.  

Therefore, statements A,B and C are consistent .

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