For a wheel spinning on an axis through its center, the ratio of the tangential acceleration of a point on the rim to the tangential acceleration of a point halfway between the center and the rim is:
A)1
B)2
C)1/2
D)4
E)1/4

Question

Quizplus · Accepted Answer

The tangential acceleration of a point on the rim is given by $a_t=r\alpha$, where $r$ is the radius of the wheel and $\alpha$ is the angular acceleration. The point halfway between the center and the rim has a radius of $r/2$, so its tangential acceleration is $(r/2)\alpha$. Therefore, the ratio of the tangential acceleration of a point on the rim to the tangential acceleration of a point halfway between the center and the rim is:

$\frac{a_t}{a_{t/2}}=\frac{r\alpha}{(r/2)\alpha}=2$

So the correct answer is B.

For a Wheel Spinning on an Axis Through Its Center