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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