You are designing a lathe motor, part of which consists of auniform cylinder who

Question

You are designing a lathe motor, part of which consists of auniform cylinder whose mass is 55 kg andwhose radius is 0.80 m that is mounted sothat it turns without friction on its axis, which is fixed. Thecylinder is driven by a belt that wraps around its perimeter andexerts a constant torque. At t = 0, the cylinder's angularvelocity is zero. At t = 25 s, its angular speed is500 rev/min. (a) What is the magnitude of the cylinder'sangular momentum at t = 25 s?
1kg·m2/s

(b) At what rate is the angular momentum increasing?
2kg·m2/s2

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

(d) What is the magnitude of the frictional force acting on the rimof the cylinder?
4 N (a) What is the magnitude of the cylinder'sangular momentum at t = 25 s?
1kg·m2/s

(b) At what rate is the angular momentum increasing?
2kg·m2/s2

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

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

Explanation / Answer

a) the magnitude of the cylinder's angular momentum att = 25 s P=I*=1/2*m*r2*=921.5 kgm2/s (b)rate is the angular momentum increasing (t)=2*500/(25*60)*t=2.09*t rad/s P/t=/t*I=2.09*1/2*m*r2=36.86kg·m2/s2 (c) the magnitudeof the torque acting on the cylinder T=I*a=2.09*I=36.86N·m (d) the magnitudeof the frictional force acting on the rim of thecylinder F*r=I*2.09 => F=46.1N (c) the magnitudeof the torque acting on the cylinder T=I*a=2.09*I=36.86N·m (d) the magnitudeof the frictional force acting on the rim of thecylinder F*r=I*2.09 => F=46.1N

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