CALC? A hollow, thin-walled sphere of mass 12.0 kg and diameter 48.0 cm is rotating about an axle through its center. The angle (in radians) through which it turns as a function of time (in seconds) is given by ?(t) = At2 + Bt4, where A has numerical value 1.50 and B has numerical value 1.10. (a) What are the units of the constants A and B? (b) At the time 3.00 s, find (i) the angular momentum of the sphere and (ii) the net torque on the sphere.
Solution 40E Step 1 of 4: For hollow thin walled cylinder,I = MR 2 2 3 a) A = 1.5 rad/s 2 and B = 1.10 rad/s 4 so that (t) will have units of radians Step 2 of 4: d b) =z dt 2 4 = d(At +Bt ) dt 3 = 2 At + 4 Bt At t = 3 s 2 4 3 z 2 (1.5 rad/s )(3 s) + 4 (1.12 rad/s )(3 s) = 128 rad/ s