machine part has the shape of a solid uniform sphere of mass 210 g and diameter

Question

machine part has the shape of a solid uniform sphere of mass 210 g and diameter 3.50 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.( NEED PART A& B)

PLEASE NOTE THIS HAS BEEN ANSWERED INCORRECTLY ALREADY

PART A IS NOT 13.6

AND

PART B ANSWER IS NOT 2.05!!

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

ANSWER:

PART B: How long will it take to decrease its rotational speed by 24.0

rad/s ?

ANSWER: t = ___________________ s

Explanation / Answer

A)
moment of inertia, I = (2/5)*m*r^2
= (2/5)*0.21 Kg*(0.035/2 m)^2
= 2.57*10^-5 Kg.m^2

Torque = f*r
= -0.02*(0.035/2) {negative because its acceleration will be negative}
= -2.5*10^-4 Nm

angular acceleration = T/I
= -(2.5*10^-4)/ (2.57*10^-5)
= -9.73 rad/s^2

B)
use:
wf= wi + a*t
wf - wi = a*t
-24 = (-9.73)*t
t = 2.47 s

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