Two uniform solid spheres have the same mass, 1.65 kg, but one has a radius of 0

Question

Two uniform solid spheres have the same mass, 1.65 kg, but one has a radius of 0.236 m while the other has a radius of 0.854 m. For each of the spheres, find the torque required to bring the sphere from rest to an angular velocity of 327 rad/s in 19.5 s. Each sphere rotates about an axis through its center. Torque on sphere with the smaller radius.

Torque on sphere with the larger radius?

For each sphere, what force applied tangentially at the equator would provide the needed torque? Force on sphere with the smaller radius?

Force on sphere with the larger radius?

Explanation / Answer

Here, angular acceleration =    327/19.5   = 16.769   rad/sec2

a) Torque on sphere with the smaller radius   = (2/5 * 1.65 * 0.236 * 0.236) * 16.769

                                                                       =   0.6164 N .m

b)   Torque on sphere with the larger radius   =   (2/5 * 1.65 * 0.854 * 0.854) * 16.769

                                                                   =      8.0717 N .m

c)    Force on sphere with the smaller radius   =   0.6164/0.236

                                                                         = 2.6118 N

d)     Force on sphere with the larger radius =   8.0717/0.854

                                                                     = 9.451 N

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