A sphere of mass 10.0 kg and radius 0.45 m is subject to an angular acceleration

Question

A sphere of mass 10.0 kg and radius 0.45 m is subject to an angular acceleration about its center of 2.00 rad/s2. A cylinder of identical mass and radius is subject to the same angular acceleration.
a. By how much will the angular momentum of the sphere change in 10 s?
b. By how much will the angular momentum of the cylinder change in 10 s?
c. How much torque did it take applied for 10 s to change these angular momenta, respectively?
d. What are the final respective rotational kinetic energies, assuming both the objects began at rest?

Explanation / Answer

MOI (sphere) = 2MR2/5 = 0.81 ; MOI (cylinder) = MR2/2 = 1.0125

a) Change in Angular momentum of sphere = MOI * * t [ = angular acceleration]

= 16.2 Js

b) For cylinder = MOI * * t = 20.25 Js

c) Time * Torque = Change in Angular momentum ; [Time = 10s]

For sphere, Torque = 1.62 Nm

For cylinder, Torque = 2.025 Nm

d) KE = MOI * * /2 ; [ = t = 20 rad/s , same for both]

KE sphere = 162 J

KE cylinder = 202.5 J

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