Question

A machine part has the shape of a solid uniform sphere of mass 250 g and a diameter of 4.30 cm. It is spinning about a frictionless axle through its center, but at one point on its equator it is scraping against metal, resulting in a friction force of 0.0200 N at that point.
PART (A):

Find its angular acceleration. Let the direction the sphere is spinning be the positive sense of rotation.

PART (B):
How long will it take to decrease its rotational speed by 21.0 Rad/s?


****NOTE: For part (A), I've tried solving using a similer question, and I got Angular Accelration = 6.59 Rad/s^2 which is wrong, according to Mastering Physics. For Part (B) I got 6.5 seconds, which is also wrong. I don't understand what I'm doing wrong since I followed the exact same method used in the same question posted on chegg. ****

Answer 1

Answer:$\alpha =9.302\ rad/s^2$

Explanation:

Given

mass of sphere $m=250\ gm$

diameter of sphere $d=4.30\ cm$

radius $r=\frac{4.30}{2}\ cm$

$f=0.0200\ N$

friction will provide resisting torque so

$f\times r=I\times \alpha$

where $I=\text{moment of Inertia}$

$f=\text{friction force}$

$\alpha =\text{angular acceleration}$

$I=\frac{2}{5}mr^2$

$0.02\times r=\frac{2}{5}mr^2\times \alpha$

$\alpha =\frac{5}{2r}\times f$

$\alpha =\frac{5}{2}\times \frac{2}{4.3\times 10^{-2}}\times 0.02$

$\alpha =9.302\ rad/s^2$

(b)time taken to decrease its rotational speed by $21\ rad/s$

$t=\dfrac{\Delta \omega }{\alpha }$

$t=\dfrac{21}{9.302}$

$t=2.25\ s$