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Equilibrium – Numerical Problem

SOLID HEMISPHERE OF RADII R EACH, are placed in contact with each other with each other with their flat faces on a rough horizontal surface. A sphere of mass m and radius R is placed symmetrically on top of them. The normal reaction between the top sphere and any hemisphere assuming the system to be in state equilibrium is

Stacked Spinning Discs Problem

Ryan asks:

“If I stack up a spinning disc on another spinning
disc. What will be the spinning RPM of the top
disc from a person’s eye on side ?”

What is the Physics involved when a cat dropped upside down lands on four legs?

If a cat is held upside down and dropped, it is able to execute a twist and to land upright, even if it has no initial angular momentum.

To Quote from Conceptual Physics by Paul G Hewitt:

“Zero-angular momentum twists and turns are performed by turning one part of the body against the other. While falling, the cat rearranges its limbs and tail several times to change its rotational inertia (moment of inertia) repeatedly until it lands feet downward. During this maneuver the total angular momentum remains zero. When it is over, the cat is not turning. This maneuver rotates the body through an angle, but it does not create continuing rotation. To do so would violate angular momentum conservation”

Question from Rotational Dynamics

Dyana Asked:

A small rubber wheel is used to drive a large pottery wheel. The two wheels are mounted so that their circular edges touch. The small wheel has a radius of 3.5 cm and accelerates at the rate of 7.9 rad/s^2, and it is in contact with the pottery wheel (radius 23.0 cm) without slipping.
a)Calculate the angular acceleration of the pottery wheel
b)Calculate the time it takes the pottery wheel to reach its required speed  of  64 rpm

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