A rigid rod of length l rotates about an axis perpendicular to the rod, with one end of the rod fixed to the axis. Which of the following are equal at all points on the rod?

I.the angular position
II.the angular velocity
III.the angular acceleration
IV.the centripetal acceleration
V.the tangential acceleration
A)I and II
B)I, II, and III
C)I, II, III and IV
D)I, II, III, IV and V
E)I, II and IV.

Question

A rigid rod of length l rotates about an axis perpendicular to the rod, with one end of the rod fixed to the axis. Which of the following are equal at all points on the rod?

I.the angular position
II.the angular velocity
III.the angular acceleration
IV.the centripetal acceleration
V.the tangential acceleration
A)I and II
B)I, II, and III
C)I, II, III and IV
D)I, II, III, IV and V
E)I, II and IV.

Quizplus · Accepted Answer

Since the rod is rigid and rotating as a single unit, all points on the rod have the same angular position, velocity, and acceleration. The centripetal acceleration and tangential acceleration are also equal at all points on the rod, given by the formulas a=cw^2 and a=rα, respectively, where c is the distance from the axis of rotation to the center of mass of the rod, w is the angular velocity, r is the distance from the axis of rotation to the point on the rod, and α is the angular acceleration. Therefore, choices I, II, and III are equal at all points on the rod, as well as choices IV and V. Hence, the correct choice is (B) I, II, and III.

A Rigid Rod of Length L Rotates About an Axis