Question

A heavy flywheel rotating counterclockwise about its middle at an original speed of 157.1 rad/s is slowing down because of friction in its bearings. a. If its acceleration is constant at 1.785 rad/s², find its angular velocity at the end of 1.00 minute. b. The flywheel is 5.50 m in diameter and has a mass of 985 kg. If the flywheel resembles a uniform disk, find the torque applied by friction.

Answer 1

Part a)

Final angular speed of the wheel is

`\omega_f = 50 rad/s`

Part b)

torque on the wheel is given as

`\tau = 6648.3 N m`

Step-by-step explanation:

Part a)

As we know that initial angular speed of the flywheel is

`\omega_i = 157.1 rad/s`

angular deceleration of the flywheel is given as

`\alpha = - 1.785 rad/s^2`

Final angular speed of the fly wheel is given as

`\omega_f = \omega_i + \alpha t`

`\omega_f = 157.1 + (-1.785)(60)`

`\omega_f = 50 rad/s`

Part b)

As we know that moment of inertia of the disc is given as

`I = (1)/(2)mR^2`

so we have

`I = (1)/(2)(985)((5.50)/(2))^2`

`I = 3724.5 kg m^2`

So torque on the wheel is given as

`\tau = I \alpha`

`\tau = 3724.5(1.785)`

`\tau = 6648.3 N m`