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You have two spheres of same mass M and radius R, one solid and one hollow, and…

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Wize University Physics Textbook (Master) > Angular / Rotational Motion

Rotational Work and Torque

4 Activities

You have two spheres of same mass M and radius R, one solid and one hollow, and an incline on which they can roll without slipping. Which one has a higher angular velocity while rolling? Show your work.

Isolid sphere=25MR2;       Ihollow sphere=23MR2I_{solid~sphere}=\frac{2}{5}MR^2; ~~~~~~~I_{hollow~sphere}=\frac{2}{3}MR^2

(PS: If you are wondering how these two spheres can have both the same mass and radius: it is because the one with less material would have a higher density. Perhaps one is made of dense steel and the other is made of a water-equivalent material.)
More Rotational Work and Torque Questions:
Forces: Torque
A wooden beam of mass 150 kg and length 10m is suspended from a horizontal wall support at the left end and connected by a cable to the same wall at the right end. The cable makes an angle of 45º with the horizontal. A person of mass 42 kg stands on the beam 2.5 m from the left wall. A 25 kg child also rests on the beam, at 7m from the left wall. Calculate (a) the tension in the rope and (b) the magnitude of the force exerted by the wall on the beam.
(Hint for part (b): there are two components. We want the magnitude, but you still need to consider both parts to find the correct magnitude.)
A spherical ball with a mass of 1kg and radius of 10cm is rolling without slipping down the track shown in the picture starting at rest. (R=2m)
b) What should be the speed of the ball when it gets to the top of the loop to be right at the verge of loosing contact with the track?
A stone of mass 9.5kg is hung vertically from the end of a rope that is wound around a pulley on a boat. The moment of inertia of the pulley is 0.47kg m2 and the radius is 0.25m. The stone is released from rest and falls toward the water, causing the pulley to rotate. After the stone has fallen 2.5 m, what is the angular velocity of the pulley?