Calculate Magnitude of Torque for Flywheel

[sealedhuman77]

Homework Statement

Massive spinning flywheels (disks) can be used for storing energy. Consider a flywheel with a diameter of 1.10 m and a mass of 510 kg. A constant force of magnitude F is applied tangentially to the rim of the flywheel to accelerate it from rest to 4.00 x 103 rev/min during 2.85 min.

(b) What magnitude of torque is necessary to cause this angular acceleration?

Homework Equations

I = mR$$^{2}$$
$$\tau$$ = I$$\alpha$$

The Attempt at a Solution

I = mR$$^{2}$$
I = (510kg)$$\ast$$(.55m)$$^{2}$$
I = 154.275 kgm$$^{2}$$

$$\tau$$ = I$$\alpha$$
$$\tau$$ = (154.275kgm$$^{2}$$)\ast(2.449rad/s$$^{2}$$
$$\tau$$ = 377.819 Nm

The answer was incorrect. Also the angular acceleration was derived from part a and is the correct number. Thanks for the help.

 

[sealedhuman77]

the Tau and Alpha symbols are not suppose to be superscripts. i screwed up the tex

 

[Moetasim]

Based on the given information, the torque required to cause the given angular acceleration can be calculated as follows:

First, we need to convert the given angular velocity from rev/min to rad/s:
4.00 x 103 rev/min = (4.00 x 103 rev/min) x (1 min/60 sec) x (2π rad/1 rev) = 418.88 rad/s

Now, using the equation τ = Iα, we can calculate the torque:
τ = Iα = (154.275 kgm2) x (418.88 rad/s2) = 64,584.6 Nm

Therefore, the magnitude of torque necessary to cause the given angular acceleration is 64,584.6 Nm.