Question

a rotating object has an angular acceleration of ( alpha = 0 \text{ rad/s}^2 ). which one or more of the following three statements is consistent with a zero angular acceleration?

a. the angular velocity is ( omega = 0 \text{ rad/s} ) at all times.
b. the angular velocity is ( omega = 10 \text{ rad/s} ) at all times.
c. the angular displacement ( \theta ) has the same value at all times.

○ a, b, and c
○ c only
○ b only
○ a only
○ a and b, but not c

Explanation:

Step1: Recall the definition of angular acceleration

Angular acceleration \(\alpha=\frac{d\omega}{dt}\). If \(\alpha = 0\ rad/s^{2}\), then \(\frac{d\omega}{dt}=0\), which means the angular velocity \(\omega\) is constant.

• For statement A: If \(\omega = 0\ rad/s\) at all times, \(\frac{d\omega}{dt}=0\), so \(\alpha=0\).
• For statement B: If \(\omega = 10\ rad/s\) at all times, \(\frac{d\omega}{dt}=0\), so \(\alpha = 0\).
• For statement C: If \(\theta\) has the same value at all times, then \(\omega=\frac{d\theta}{dt}=0\) (since the derivative of a constant is zero). And if \(\omega = 0\) (constant), then \(\alpha=\frac{d\omega}{dt}=0\)

Answer:

A, B, and C