A uniform spherical shell of mass M = 12 kg and radius R = 28 cm rotates about a

Question

A uniform spherical shell of mass M = 12 kg and radius R = 28 cm rotates about a vertical axis on frictionless bearings (Figure 10-47). A massless cord passes around the equator of the shell, over a pulley of mass 1 kg and radius r = 12 cm, and is attached to a small object of mass m = 10 kg. There is no friction on the pulley's axle and the cord does not slip on the pulley. Treat the pulley as a disk.

(a) What is the linear speed of the hanging mass after falling a distance of 3 meters?
m/s

(b) What is the angular speed of the spherical shell at this time?
rad/s

(c) What is the angular speed of the pulley at this time?

Explanation / Answer

a)

conserving energy,

v = sqrt((10*9.8*3)/(0.5*10+0.5*(2*12/3)+0.5*(0.5*1))) = 5.63 m/s

b)

angular speed = 5.63/0.28 = 20.13 rad/s

c)

angular speed = 5.63/0.12 = 46.91 rad/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.