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Dmitrij [34]
3 years ago
13

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 frictionl

ess 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. ****
Physics
1 answer:
zysi [14]3 years ago
6 0

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

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