# Newtonian Mechanics

**Rolling Down an Incline**

### What it shows:

An object rolling down a hill acquires both translational and rotational kinetic energy. One must take the rotational kinetic energy into account when calculating the object's velocity at the bottom of the hill

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Read more about Rolling Down an Incline**Yo-yo**

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 r_{1}F rotating the yo-yo counter-clockwise. Pulling the string horizontally as in (b) creates a...

**Torsion Pendulum**

Determination of the moment of inertia by period measurements.

**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:...

Read more about Tennis Racquet Flip**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

\(T...

Read more about Hula Hoop Rotational Inertia**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...

Read more about Parallel-Axis Theorem**Suitcase Gyro**

A motor driven gyro hidden in a suitcase gives surprising results when the suitcase is moved.

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Read more about Suitcase Gyro**Tail Wags Dog**

Lecturer tries to swing baseball bat while standing on turntable.

**Flyball Governor**

Rotating balls change speed as radius of rotation is changed.

**Coffee Mug on a String**

### What it shows:

Conservation of angular momentum and the exponential increase in friction are what save the coffee mug from smashing into the floor. Use this entertaining demonstration to introduce either of those physics concepts.

### How it works:

You need a pencil, a pen, a china cup (we use a china cup to add suspense and a threat of disaster), and about 1 meter of string. Tie one end of the string to the cup and the other to the pen. Hold the pencil in one hand and drape the string over it so the cup hangs down a few centimeters. Hold the pen with your other hand (arm...

Read more about Coffee Mug on a String**Orbiter**

Ball on string orbits with increasing speed as string is shortened.

### What it shows:

An object moving in a circular orbit of radius r has an angular momentum given by:

L = r × mv = mr^{2}ω.

A simple way to show conservation of angular momentum is a ball on a string, whirled around your head. As you change the length of the string, the ball's orbital speed changes to conserve angular momentum.

### How it works:

The orbiter consists of a meter length of cord with a wooden ball at one end and a wooden anchor at the other. The cord passes...

Read more about Orbiter**Three Dumbbells**

Lecturer rotates on turntable whilst holding two dumbbells.

### What it shows:

Angular momentum, the product of a body's moment of inertia and angular velocity, is always conserved. A reduction in moment of inertia will result in a proportional rise in angular velocity.

### How it works:

A volunteer holds the other two dumbbells ^{1} in each hand and stands upon a rotating platform. ^{2} With arms outstretched and a little push they begin to rotate at a certain angular velocity. By pulling in their arms to their chest, the moment of inertia is...

**Crashing Pendulum**

A pendulum is allowed to "crash" into a bar, dramatically altering its motion, but energy is conserved as is evidenced by the return swing.

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