A wheel (solid/cylinder) is free to rotate about its axis that is not frictionle

Question

A wheel (solid/cylinder) is free to rotate about its axis that is not frictionless and is initially at rest it has a moment of inertia I = 20 kgm^2. A constant external torque of T_applied = 60 N middot m is applied to the wheel for t_1 = 20 secs [keep in mind, there is an unknown constant frictional torque also being applied during this time interval], at the end of the 20 seconds, the wheel has an angular velocity of omega = 50 rad/sec. Then the external torque is removed (leaving only the frictional torque), and the wheel comes to rest a certain number of seconds (t_2) later. a) Calculate the frictional torque (T_fr), which is assumed to be constant (with the correct unit) b) Calculate the time (t_2) in seconds that it takes to slow down when only acted upon by the frictional torque.

Explanation / Answer

Using Net torque is Tnet = I*alpha

I is the moment of inertia = 20 kg-m^2

alpha is the angular accelaration

alpha = (w-wo)/t = (50-0)/20 = 2.5 rad/s^2

Tnet = Texeternal - T_frictional = I*alpha

60-T_frictional = 20*2.5

T_frictional = 60-(20*2.5) = 10 N-m is the frictional torque

b) for the t2 seconds

initial angular speed is wo = 20 rad/sec

final angular velocity is W = 0 rad/sec

time taken is t = t2= ?

Tnet = T_frictional = 10 N-m

then Using Tnet = I*alpha

-10 = 20*(W-wo)/t2

-10 = 20*(0-20)/t2

t2 = 40 sec

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