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 105 kg and whose radius is 0.60 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? _____ kgm2/s (b) At what rate is the angular momentum increasing?________ kgm2/s2 (c) What is the magnitude of the torque acting on the cylinder? Nm (d) What is the magnitude of the frictional force acting on the rim of the cylinder?______ N

Explanation / Answer

a) L = I w = (1/2 M R^2) w = (0.5*105*0.6^2)(550*2*pi/60)=1088.6 b) dL/dt = 1088.6/25=43.54 c) torque = dL/dt = 43.54 d) torque = r F F = torque/r = 43.54/0.6=72.57 N

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