A large grinding wheel in the shape of a solid cylinder of radius 0.330 m is free to rotate on a frictionless, vertical axle. A constant tangential force of 300 N applied to its edge causes the wheel to have an angular acceleration of 1.072 rad/s2.

(a) What is the moment of inertia of the wheel?

(b) What is the mass of the wheel?

(c) If the wheel starts from rest, what is its angular velocity after 4.00 s have elapsed, assuming the force is acting during that time?

To find the answers to these questions, we can use the formulas related to rotational motion. I'll explain the steps for each question:

(a) Moment of inertia can be calculated using the formula:
Moment of Inertia = (Mass) * (Radius^2)

Since we don't have the mass of the wheel, we need to find it first using the given information.

(b) We can find the mass of the wheel using the formula:
Torque = (Moment of Inertia) * (Angular acceleration)

The torque can be calculated using the formula:
Torque = (Force) * (Radius)

(c) To find the angular velocity after a given time, we can use the formula:
Angular velocity = Initial angular velocity + (Angular acceleration) * (Time)

Now, let's calculate each part of the problem:

(a) What is the moment of inertia of the wheel?

Given:
Radius (r) = 0.330 m

We need to find the mass of the wheel first:

From (b), using the formula:
Torque = (Moment of Inertia) * (Angular acceleration)
Torque = (Force) * (Radius)
300 N * 0.330 m = Mass * (Radius^2) * 1.072 rad/s^2

Solving this equation will help us find the mass of the wheel.

(b) What is the mass of the wheel?

Using the equation derived in part (a), now we have the mass of the wheel.

(c) If the wheel starts from rest, what is its angular velocity after 4.00 s have elapsed, assuming the force is acting during that time?

Given:
Time (t) = 4.00 s

We can use the formula:
Angular velocity = Initial angular velocity + (Angular acceleration) * (Time)
Since the wheel starts from rest, the initial angular velocity is zero.

With this equation, we can find the angular velocity after 4.00 s have elapsed.

torque = F*r = I*alpha

where F = force, r = radius, I = moment of inertia, and alpha is angular acceleration.

a)
For a cylinder I = 1/2*m*r^2, where m is mass
b)
F*r = 1/2*m*r^2*alpha

Substitute values from the problem to find m
c) omega = alpha*t
where omega is angular velocity