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

Answer:

Part a)

Final angular speed of the wheel is

$\omega_f = 50 rad/s$

Part b)

torque on the wheel is given as

$\tau = 6648.3 N m$

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

$I = \frac{1}{2}mR^2$

so we have

$I = \frac{1}{2}(985)(\frac{5.50}{2})^2$

$I = 3724.5 kg m^2$

So torque on the wheel is given as

$\tau = I \alpha$

$\tau = 3724.5(1.785)$

$\tau = 6648.3 N m$