Question

A uniform disk of radius 0.2 m and mass m = 16 kg is mounted on a nearly frictionless axle. A string is wrapped tightly around the disk and pulled with a constant force of F = 1 N. After a while the disk has reached an angular speed of ω0 = 2.3 rad/s. What is its angular speed 1.5 s later?

Answer 1

Since the force is constant, so the torque due to this force will also be constant.

So, when the torque is constant that means the angular acceleration will also be constant.

So, moment of inertia of the disk

I=0.5mr²

I=0.5*16*0.2²

I=0.32 kg.m²

Now that torque is,

T=F.r

=1*0.2

=0.2 N-m

Also we know that,

Torque= (Moment of inertia)*(Angular acceleration)

So,

Angular acceleration=0.2/0.32

=0.625

Now applying first equation of angular motion,

=2.3+(0.625*1.5)

=3.2375 rad/sec