Rotational Dynamics (moment of inertia and the action of torques)

Center of Percussion

The motion (or lack of motion) of the suspension point of an object is observed when the object is struck a blow.

What it shows

The center of percussion (COP) is the place on a bat or racket where it may be struck without causing reaction at the point of support. When a ball is hit at this spot, the contact feels good and the ball seems to spring away with its greatest speed and therefore this is often referred to as the sweet spot. At points other than this spot, the bat or racket may vibrate or even sting your hands. This experiment shows the effect by demonstrating what...

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A very large cable spool (or smaller version) is made to roll in either direction or slide, depending on the angle of pull; action of a torque.

What it shows:

Depending upon the angle of applied force, a yo-yo can be made to roll forwards, backwards or simply slide without rotating.

How it works:

The effect of force angle is illustrated in figure 1; (a) and (b) are the extreme cases. For (a), pulling the string vertically creates a torque r1F rotating the yo-yo counter-clockwise. Pulling the string horizontally as in (b) creates a...

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Tennis Racquet Flip

What it shows:

A simple and convincing demonstration of the intermediate axis theorem. Consider an object (a tennis racquet in this case) with three unequal principle moments of inertia. If the racquet is set into rotation about either the axis of greatest moment or least moment and is thereafter subject to no external torques, the resulting motion is stable. However, rotation about the axis of intermediate principle moment of inertia is unstable — the smallest perturbation grows and the rotation axis does not remain close to the initial axis of rotation.

How it works:...

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Hula Hoop Rotational Inertia

What it shows:

A suspended hula hoop has the same period of oscillation as a pendulum whose length is equal to the diameter of the hoop.

How it works:

The parallel-axis theorem allows us to readily deduce the rotational inertia of a hoop about an axis that passes through its circumference and is given by

\(I = I_{cm} + MR^2 = 2MR^2\)

where M is the mass of the hoop and R is its radius. The period of oscillation thus becomes


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Parallel-Axis Theorem

What it shows:

One can show that the period of oscillation of an object doesn't change for different suspension points, as long as they're the same distance from the COM. This is consistent with what the parallel-axis theorem tells us about the moment of inertia of the object.

How it works:

The parallel-axis theorm states that if \(I_{cm}\) is the moment-of-inertia of an object about an axis through its center-of-mass, then \(I\), the moment of inertia about any axis parallel to that...

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