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 95 kg and whose radius is 0.80 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 550 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

a.)
angular momentum (L)=Iw=moment of inertia (kind of like the angular equivalent of mass) times angular velocity

I=(1/2)MR^2 for a uniform cylinder
w=550rev/min
550x 2pi/60sec=57.59rad/sec
L=((1/2)(95)(.8)^2) x (57.59) = 1750.7

b.)
rate=change in L / change in time=1750.7/25sec
=70.02

c.)
T=dL/dt=70.02the same as part b

d.)
T = Fr
F = T/r = 70.02/0.6 = 116.7N

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