Question

In: Physics

A compost barrel can be considered as a solid cylinder of mass 50.0 kg and radius...

A compost barrel can be considered as a solid cylinder of mass 50.0 kg and radius of r = 30.0 cm, and a length of 0.900 m. It can be turned about the long axis by applying a force to a handle located d = 20.0 cm from the axis of the cylinder. The compost barrel needs to be turned through 250 complete revolutions. Assume you can apply a constant force of F = 10.0 N (always perpendicular to the radius as the handle goes around in a circle).
What is the angular acceleration of the barrel?
How much time does it take to turn the barrel through 250 rev?
What is the angular velocity of the barrel at the end of that time? Is this reasonable?

Expert Solution

Given,

mass of cylinder is

radius of cylinder is

length of cylinder is

Moment of Inertia of the cylinder is

Torque applied to the cylinder is

Let be its angular acceleration, we have

One complete revolution is , therefore in 250 revolutions,

angular distance covered is

Assuming initially at rest, we have initial angular velocity

Let the time taken by the barrel be , then we have

Let be the final angular velocity, then we have

This is the final angular velocity attained by the cylinder in 250 revolutions

genius_generous answered 2 years ago

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