Question

A grinding wheel is a uniform cylinder with a radius of 7.50 cm and a mass of 0.670 kg .

Part A Calculate its moment of inertia about its center. Express your answer to three significant figures and include the appropriate units.

Part B Calculate the applied torque needed to accelerate it from rest to 1750 rpm in 7.80 s . Take into account a frictional torque that has been measured to slow down the wheel from 1500 rpm to rest in 53.0 s . Express your answer to three significant figures and include the appropriate units.

Answer 1

(A)

Moment of inertia about wheel's center-

l = MR^2 / 2

l = 0.67*(0.075)^2 / 2

l = 1.88*10^(-3) kg.m^2

(B)

Accelerational torque,

a = l* = l*w / t

a = 1.88*10^(-3)*(1750*2*pi / 60*7.8)

a = 0.0441 N.m

Frictional torque,

f = 1.88*10^(-3)*(1500*2*pi / 60*53)

f = 0.00557 N.m

Net  applied torque,

= a + f

= 0.0441 + 0.00557

= 0.0497 N.m