Question

A motor drives a disk initially at rest through 24.4 rotations in 5.0s. Assume the vector sum of the torques caused by the force exerted by the motor and the force of friction is constant. The rotational inertia of the disk is 4.0 kg*m^2. When the motor is switched off, the disk comes to rest in 12s.

A) What is the magnitude of torque created by the force of friction?

B) What is the magnitude of torque caused by the force exerted by the motor?

Answer 1

let wo = 0

let alfa is the angular acceleration when motor is switched on.

angular displacement,

theta = wo*t + (1/2)*alfa*t^2

24.4*2*pi = 0 + (1/2)*alfa*5^2

==> alfa = 24.4*2*pi*2/5^2

= 12.3 rad/s^2

angular speed of the disk bofore the motor is swirched on,

w = wo + alfa*t

= 0 + 12.3*5

= 61.5 rad/s

angular acceleration when the motor is switched off,

alfa' = (wf - w)/t

= (0 - 61.5)/12

= -5.125 rad/s^2

A) the magnitude of torque created by the force of friction, T_friction = I*|alfa'|

= 4.0*5.125

= 20.5 N.m <<<<<<<<<------------Answer

B) when the motor is switched on, Tnet = I*alfa

T_motor + T_friction = 4*12.3

T_motor - 20.5 = 49.2

T_motor = 49.2 + 20.5

= 69.7 N.m <<<<<<<<<------------Answer