Two uniform solid spheres have the same mass, 1.55 kg, but one has a radius of 0

Question

Two uniform solid spheres have the same mass, 1.55 kg, but one has a radius of 0.266 m while the other has a radius of 0.834 m. For each of the spheres, find the torque required to bring the sphere from rest to an angular velocity of 307 rad/s in 14.5 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

wf = wi + alpha*t

wi =0

307 = 0 + alpha * 14.5

alpha = 21.17 rad/s^2

torque = I*alpha

I for solid sphere = 2mr^2/5

for smaller radius sphere

t = 0.9288 N-m

for larger radius sphere

t = 9.13 N-m

now we know that

t = F*r

for smaller radius

F = t/r

F = 3.49 N

for larger radius sphere

F = t/r

F = 10.95 N

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