A flywheel has shape as a homogeneous cylinder with mass m = 40,0 kg and radius r = 0,50 meters. The cylinder is rotating round the axis of symmetry, and is runned by a motor with constant angular velocity (w0). When the motor is switched off, the cylinder is affected by a moment of force that are caused by friction.
How long will the cylinder rotate before the angular velocity is halved?
The friction: M = -kw
w = omega
k = (1,2 * 10^2) Nm/s
The Attempt at a Solution
The moment of inertia: I = (m*r^2)/2 (cylinder)
M = -kw => 1) w = -(M/k)
w = 1/2*w0
alpha = w/T = (1/2*w0)/T
1) (1/2*w0) = -(M/k)
(1/2*w0) = -((I*alpha)/k)
(1/2*w0) = -((((m*r^2)/2)*((1/2*w0)/T))/k)
When solving this equation the answer is: T = -416
BUT sadly we are quite sure this answer is incorrect, any help will be appreciated.