You are designing a lathe motor, part of which consists of a uniform cylinder wh

Question

You are designing a lathe motor, part of which consists of a uniform cylinder whose mass is 135 kg and whose radius is 0.50 m that is mounted so that it turns without friction on its axis, which is fixed. The cylinder is driven by a belt that wraps around its perimeter and exerts a constant torque. At t = 0, the cylinder's angular velocity is zero. At t = 25 s, its angular speed is 500 rev/min.

(a) What is the magnitude of the cylinder's angular momentum at t = 25 s?
kg·m2/s

(b) At what rate is the angular momentum increasing?
kg·m2/s2

(c) What is the magnitude of the torque acting on the cylinder?
N·m

(d) What is the magnitude of the frictional force acting on the rim of the cylinder?
N

Explanation / Answer

moment of inertia of cylinder, I = 0.5mr^2 = 0.5*135*0.5^2 = 16.875
a) Angular momentum = Iw
w = 500 rev per min = 500*2pi/60 rad/sec
Angular momentum = 16.875*500*2*3.14/60 = 883.125 kg m^2 / s

b) Rate of change of angular momentum = Ia (where a = angular acceleration)
now, v = u + at
v = 500*2*pi/60
u = 0
a = ?
t = 25s
so a = 2.093

rate = 16.875*2.093 = 35.325 kg m^2 / s^2

c) Torque = Ia =35.325 Nm
d) T = f*r
f = 35.325/0.5 = 70.65 N

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