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 55 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 450 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 = 450 rev/min
450 x 2pi / 60sec = 47.1 rad/sec
L=((1/2)(55)(0.5)^2) x (47.1) = 323.81 kg.m^2 / s^2

b.)
rate = change in L / change in time

= 323.81 / 25 sec
= 12.95

c.)
T= dL/d

t = 12.95 the same as part b

d.)
T = Fr
F = T/r = 12.95 / 0.5 = 25.9 N

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