A wheel free to rotate about its axis that is not frictionless is initially at r

Question

A wheel free to rotate about its axis that is not frictionless is initially at rest. A constant external torque of +58 N·m is applied to the wheel for 22 s, giving the wheel an angular velocity of +510 rev/min. The external torque is then removed, and the wheel comes to rest 120 s later. (Include the sign in your answers.)

The answers are a) 20.2 kg*m^2

and b) -8.99 N*m

(a) Find the moment of inertia of the wheel.

answer is 20.2, how did they find the answer

(b) Find the frictional torque, which is assumed to be constant.

-8.99 how did they find the answer

Explanation / Answer

Here ,

a)

let the moment of inetia is I

wf = 510 rev/min

wf = 510 * 2pi/60

wf = 53.4 rad/s

Now , time taken to stop is ts = 120 s

angular acceleration due to friction

af = wf/t

af = -53.4/120

af = - 0.445 rad/s^2

Now , while accelerating

angular acceleration is a

a = wf/t

a = 53.4/22 = 2.43 rad/^2

Now , for the moment of inertia

T = I * (a - af)

58 = I * (2.43 + 0.445)

I = 20.2 Kg.m^2

the moment of inertia is 20.2 Kg.m^2

part B)

frictional torque = I * af

frictional torque = - 20.2 * 0.445

frictional torque = -8.99 N.m

the frictional torque acting is -8.99 N.m

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