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`

Step-by-step explanation:

Given

mass of sphere
`m=250\ gm`

diameter of sphere
`d=4.30\ cm`

radius
`r=(4.30)/(2)\ cm`

`f=0.0200\ N`

friction will provide resisting torque so

`f* r=I* \alpha`

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

`f=\text{friction force}`

`\alpha =\text{angular acceleration}`

`I=(2)/(5)mr^2`

`0.02* r=(2)/(5)mr^2* \alpha`

`\alpha =(5)/(2r)* f`

`\alpha =(5)/(2)* (2)/(4.3* 10^(-2))* 0.02`

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

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

`t=(\Delta \omega )/(\alpha )`

`t=(21)/(9.302)`

`t=2.25\ s`