# Calculating Torque & Work on a Flywheel of Mass 183kg & Radius 0.63m

• bobby3280
The kinetic energy of a rotating mass is given by the equation KE = 1/2 * I * w^2, where I is the moment of inertia and w is the angular velocity. In this case, the initial angular velocity is 0 and the final angular velocity is 120 rpm, or 12.56 rad/s. Plugging in the values, we get KE = 1/2 * 26.65 * (12.56)^2 = 1.68 kJ. So in summary, the work done during the 34.3 s is 1.68 kJ.
bobby3280
A flywheel of mass 183 kg has an effective radius of 0.63 m (assume the mass is concentrated along a circumference located at the effective radius of the flywheel).

(a) What torque is required to bring this wheel from rest to a speed of 120 rpm in a time interval of 34.3 s?

(b) How much work is done during the 34.3 s?

Alright I figured out (a) using the moment of Inertia and the angular acceleration to be 26.65 N * m

So for part (b) I tried using W = torque * theta
to find theta i used many ways all coming up with right around 432 rad
so W = 26.65 * 432
= 11.5 kj
But this answer isn't correct any suggestions as to where i went wrong??

All the work done on the flywheel is converted to rotational energy. Do you know an equation that will give you the energy of a rotating mass?

Hope this helps,
Sam

For (b), simply use the fact that the work done equals the change of kinetic energy.

## 1. How do you calculate torque on a flywheel?

To calculate torque on a flywheel, you need to know the force applied to the flywheel and the distance from the center of the flywheel to the point where the force is applied. The formula for torque is T = F x r, where T is the torque, F is the force, and r is the distance.

## 2. What is the formula for calculating work on a flywheel?

The formula for calculating work on a flywheel is W = T x θ, where W is the work, T is the torque, and θ is the angular displacement of the flywheel in radians. This formula takes into account the rotational motion of the flywheel.

## 3. How do you convert angular velocity to linear velocity?

To convert angular velocity (ω) to linear velocity (v), you can use the formula v = rω, where r is the radius of the flywheel. This formula takes into account the distance traveled by a point on the edge of the flywheel in one revolution.

## 4. How does the mass of a flywheel affect its torque and work?

The mass of a flywheel does not directly affect its torque and work, as these values are dependent on the applied force and the distance from the center of the flywheel. However, the mass of a flywheel can affect its moment of inertia, which is a measure of its resistance to changes in rotational motion. A higher mass can result in a higher moment of inertia, which can affect the amount of torque and work required to change the flywheel's angular velocity.

## 5. How do you calculate the moment of inertia of a flywheel?

The formula for calculating the moment of inertia (I) of a flywheel is I = ½mr², where m is the mass of the flywheel and r is the radius. This formula can be used for a solid disk flywheel, which is the most common type. For other shapes, such as a ring or cylinder, different formulas may be used.

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