Question

A uniform-density 7 kg disk of radius 0.21 m is mounted on a nearly frictionless axle. Initially it is not spinning. A string is wrapped tightly around the disk, and you pull on the string with a constant force of 44 N through a distance of 0.9 m. Now what is the angular speed? ωf= radians/s the tolerance is +/-5%

Answer 1

Answer:

The final angular speed becomes $264rad/sec$

Explanation:

The work done by the force shall appear as the rotational kinetic energy of the system.

We know that work done by force is given by

$W=Force\times displacement\\\\W=44\times 0.9=39.6Joules$

Now the rotational kinetic energy of the disc equals

$K.E=\frac{1}{2}I\omega ^{2}$

We know that moment of inertia of disc is given by

$I=\frac{1}{2}mr^{2}$

Thus applying values we get

$39.6=\frac{1}{2}\times 7\times.21^{2}\times \omega _{f}\\\\\therefore \omega _{f}=\frac{39.6}{0.15}=264rad/sec$