Two uniform solid spheres have the same mass of 1.95 kg, but one has a radius of
ID: 2064942 • Letter: T
Question
Two uniform solid spheres have the same mass of 1.95 kg, but one has a radius of 0.230 m while the other has a radius of 0.859 m. Each can rotate about an axis through its center.(a) What is the magnitude ? of the torque required to bring the smaller sphere from rest to an angular speed of 317 rad/s in 15.5 s?
(b) What is the magnitude F of the force that must be applied tangentially at the sphere's equator to provide that torque?
(c) What is the corresponding value of ? for the larger sphere?
(d) What is the corresponding value of F for the larger sphere?
Explanation / Answer
I = (2/5)mr^2
= I
a) = 317/15.5 = 20.45rad/s^2
= (2/5)*1.95*0.23^2*20.45 = 0.84N-m
b) F = /r = 0.84/0.23 = 3.65N
c) = (2/5)*1.95*0.859^2*20.45 = 11.77N-m
d) F = 11.77/0.859 = 13.7N
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