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

Question

A 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)

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

Soluution: From the question we have:

A 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

now lets solve

1. Moment of inertia of solid sphere
= (2/5).(0.21).(0.0175^2) kg.m^2 = 2.57 x 10^-5 kg.m^2

Hence, angular acceleration = 0.02 x 0.0175/2.57x10^-5 rad/s^2 = 13.6 rad/s^2

2. Time taken = 28/13.6 s = 2.06 s

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