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 250 N applied to its edge causes the wheel to have an angular acceleration of 1.053 rad/s2.

(a) What is the moment of inertia of the wheel?
kg · m2

(b) What is the mass of the wheel?
kg

(c) If the wheel starts from rest, what is its angular velocity after 5.00 s have elapsed, assuming the force is acting during that time?
rad/s

To answer these questions, we need to use the formulas related to rotational motion. Let's go step by step:

(a) The moment of inertia of the wheel can be calculated using the formula:

Moment of Inertia (I) = (angular acceleration) / (angular velocity)

In this case, the angular acceleration is given as 1.053 rad/s^2. To find the angular velocity, we first need to calculate the time it takes for the wheel to reach that speed.
The formula to find the time is:

angular acceleration = (change in angular velocity) / (time)

From the given data, the change in angular velocity is (angular velocity) - (initial angular velocity), and the initial angular velocity is 0 since the wheel starts from rest. Therefore:

1.053 rad/s^2 = (angular velocity) / (time)

Given that time is 5.00 s, we can rearrange the equation to solve for angular velocity:

(angular velocity) = (angular acceleration) * (time)

Substituting the values:

(angular velocity) = 1.053 rad/s^2 * 5.00 s
(angular velocity) = 5.265 rad/s

Now we can calculate the moment of inertia:

Moment of Inertia = (1.053 rad/s^2) / (5.265 rad/s)
Moment of Inertia = 0.2 kg · m^2

Therefore, the moment of inertia of the wheel is 0.2 kg · m^2.

(b) To find the mass of the wheel, we can use the formula:

Moment of Inertia = (mass) * (radius)^2

Rearranging the formula, we have:

mass = (Moment of Inertia) / (radius^2)

Substituting the values:

mass = 0.2 kg · m^2 / (0.330 m)^2
mass = 1.82 kg

Therefore, the mass of the wheel is 1.82 kg.

(c) To find the final angular velocity after 5.00 s, we can use the formula:

Final angular velocity = (initial angular velocity) + (angular acceleration) * (time)

Given that the initial angular velocity is 0, and the angular acceleration is 1.053 rad/s^2:

Final angular velocity = 0 + (1.053 rad/s^2) * (5.00 s)
Final angular velocity = 5.265 rad/s

Therefore, the angular velocity of the wheel after 5.00 s is 5.265 rad/s.