In: Physics
A uniform disk of mass 371 kg and radius 0.19 m is mounted on frictionless bearings so it can rotate freely around a vertical axis through its center (see the following figure). A cord is wrapped around the rim of the disk and pulled with a force of 10 N. What is the angular velocity (in rad/s) at the instant the disk has completed four revolutions. The disk starts from rest.
Group of answer choices
3.78 rad/s
3.87 rad/s
2.35 rad/s
2.53 rad/s
Answer :Angular velocity ,
Explanation:
Distance covered in 4 revolutions,
Work done by the force (F=10N) to make 4 revolutions,
When an object is rotating about its center of mass, its rotational kinetic energy ,
where I is the moment of Inertia, for the disk and is the angular velocity
i.e
Work done by the force (F=10N) to make 4 revolutions will be equal to the rotational kinetic energy .
i.e
Substituting the values and ,