Question

A machine part has the shape of a solid uniform sphere of mass 225 g and diameter 3.00 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.
(a) Find its angular acceleration.
(b) How long will it take to decrease its rotational speed by 22.5 rad/s?

Answer 1

Answer: a) angular acceleration(alpha)=-14.8rad/s^2

b) time taken (t) = 1.52s

Explanation:

What we are given

Mass of the solid sphere m =225g = 0.225kg

Diameter D = 3.00cm = 0.0300m

Radius = D/2 = 0.01500m

Frictional Force = 0.0200N

a) to determine the angular acceleration, we first calculate the torque, then moment of inertia, before the angular acceleration.

Torque = -fr

= - (0.0200)(0.01500)

=-3.00X10^-4Nm

Moment of inertia I

= 2/5mr^2

=2/5(0.225)(0.01500)^2

=2.025X10^-5kgm^2

Angular acceleration (alpha)= torque/moment of inertia (I)

= -3.00X10^-4Nm/2.025X10^-5kgm^2

=-14.8rad/s^2

b) time taken (∆t) = w/alpha

w= -22.5rad/s

Angular acceleration (alpha) = -14.8rad/s^2

∆t = -22.5/-14.8

= -1.52s