12. A) Two uniform solid spheres have the same mass, 1.45 kg , but one has a rad

Question

12.

A) Two uniform solid spheres have the same mass, 1.45 kg, but one has a radius of 0.236 m while the other has a radius of 0.864 m. For each of the spheres, find the torque required to bring the sphere from rest to an angular velocity of 347 rad/s in 18.5 s. Each sphere rotates about an axis through its center. Torque on sphere with the smaller radius.

B) Torque on sphere with the larger radius.

C) For each sphere, what force applied tangentially at the equator would provide the needed torque? Force on sphere with the smaller radius.

D) Force on sphere with the larger radius.

Explanation / Answer

here , for a solid sphere ,

moment of inertia = 0.4MR^2

Now , let angular acceleration be a

using first equation of motion

347 = a * 18.5

a = 18.76 rad/s^2

A)

Now , for the smaller sphere ,

I = 0.4 * 1.45 * 0.236^2

I = 0.0323 Kg.m^2

Now, using second law of motion

Torque = I*a

Torque = 0.0323 * 18.76

Torque = 0.606 N.m

B) for the larger sphere ,

I = 0.4 * 1.45 * 0.864^2

I = 0.433 Kg.m^2

Now, using second law of motion

Torque = I*a

Torque = 0.433 * 18.76

Torque = 8.122 N.m

C)

Now, Torque = F * R

for the smaller sphere ,

0.606 = F * 0.236

F = 2.56 N

D)

For the larger sphere ,

8.122 = Fl * 0.864

F1 = 9.4 N

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