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Theorem of parallel axis

State the theorem of parallel axes for the moment of inertia.


Ref http://hyperphysics.phy-astr.gsu.edu/hbase/parax.html

Physics of Diving

When a high diver in a swimming event springs from the board and “tucks in”, a rapid spin result. Why is this?

Answer: This is the consequence of conservation of angular momentum.

The angular momentum of a body is the product of Moment of inertia (A measure of rotational inertia and it depends on the mass as well as distribution of mass about the axis of rotation. Farther the masses, greater will be the rotational inertia) and the angular velocity (The speed of rotation)

The angular momentum of a body remains unchanged in the absence of any external torque.

When the diver dives, he is giving his body a turning and takes off with his limbs stretched. In the stretched position, the moment of inertia is more. When he “tucks in”, the moment of inertia decreases. But since this happens without any external torque, it would result in an increase in angular velocity so as to keep the angular momentum constant.

How wheel + Tyre diameter affects a vehicle’s speed

I have been told a larger wheel/tyre decrease acceleration because its harder to turn the wheel making the car rev slower.

But the same person tells me it will increase the top speed.

My question is if the car has a max rev of 8000rpm but only reaches 7000rpm in its highest gear would a smaller wheel/tyre not make it easier for the car to rev higher thus possible increasing the top speed by using a smaller wheel?

(Garry asked)

As wheel radius increases, its top speed increases for a given RPM since for a given RPM the speed of the vehicle is directly proportional to its radius.
The distance traveled in one rotation = 2 π R
But now, there is another effect also here. As the radius of tyre increases, its moment of inertia increases and it would be harder for the engine to rotate it. So, the engine will not be able to turn it with the same ease as before, but however, there will be an increase in top speed other conditions remaining the same.
Monster Truck
Refer to http://wahiduddin.net/calc/calc_speed_rpm.htm for a calculation of top speed vs tyre radius

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”

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March 2021

Schrodinger’s Cat in Daily Life

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