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## Homework Statement

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 is caused by friction.

When the motor is being swiched off, the rotational frequency of the cylinder was 5000 rpm. How many revolutions does the cylinder make before it stops?

## Homework Equations

The friction: M = -kw

w = omega

k = (1,2 * 10^2) Nm/s

w0 = 5000 rpm

## The Attempt at a Solution

The moment of inertia: I = (m*r^2)/2 (cylinder)

M = -kw => 1) w = -(M/k)

w = 1/2*5000

alpha = w/T = (1/2*w0)/T

1) (1/2*w0) = -(M/k)

(1/2*w0) = -((I*alpha)/k)

Any help will be appreciated :)