A long thin rod of length 2L rotates with a constant angular acceleration of 8.0 rad/s2 about an axis that is perpendicular to the rod and passes through its center.
-What is the ratio of the tangential acceleration of a point on the end of the rod to that of a point a distance L/2 from the end of the rod?
A)1:1
B)1:2
C)2:1
D)4:1
E)1:4

Question

Quizplus · Accepted Answer

The tangential acceleration is given by $ a_t = \alpha \times r $, where $ \alpha $ is the angular acceleration and $ r $ is the distance from the axis of rotation. For a point at the end of the rod, $ r = L $, and for a point at $ L/2 $ from the end, $ r = L/2 $. Thus, the ratio is $ L : (L/2) = 2:1 $.

A Long Thin Rod of Length 2L Rotates with a Constant