The hinged stick is held in place as shown with the ball balanced on the end of the stick. When the stick is released, it accelerates faster than the ball, so the ball falls into the cup.

Note that the initial position of the ball is directly above the final position of the cup!

Download the mpeg below for a brief clip of the demonstration in action.

Two wooden sticks, when toppled by a very gentle push (about one-third of the way down from the top), break up with rotation of the upper half lagging behind that of the lower half. This is similar to the breakup of real chimneys when they are toppled.

Click on the link below to see an mpeg video of the action.

Two physical pendula, one of which has a weight on its bottom end, are held in a horizontal position and released from rest simultaneously. Q: Which one will reach the bottom first, or will it be a tie. A: The one without the weight will accelerate faster and reach the bottom first. This can be a rather tricky question, requiring careful analysis by the student. Mislead them by pointing out that pendula of the same length have the same period!

In this apparatus the position of the weight can be adjusted and set using a thumbscrew. Q: Where must the bob be placed so that the two pendula will accelerate at the same rate and reach the bottom simultaneously? A: At one-third of the distance from the bottom end. The period of a physical pendulum is equal to that of a simple pendulum with two-thirds of the length of the physical pendulum.

The bat is held at the small end and struck soundly with the mallet at the bigger end. A yellow marker marks the location of the center of percussion. When the bat is struck below the center of percussion it will spin out of the holder's fingers moving in the opposite direction to that of the incoming mallet. When the bat is struck above the center of percussion it will spin out of the holder's fingers moving the same direction as the incoming mallet. When the bat is struck at the center of percussion it will rotate about the holder's fingers, but will not spin out of the fingers.

This illustrates how a ball player wants to hit the baseball to get the greatest momentum transfer to the ball with the least reaction force on the batter's hands and arms. A tennnis stroke works the same way. You can minimize "tennis elbow" by hitting the ball at the center of percussion of the racket so that the rotational reaction on your wrist and elbow is minimized.

Click your mouse here to see the collision of a baseball and a softball with composite bats, taken by a slow motion camera.

Click your mouse here to see the vibrational modes of a baseball bat.

A mass m is attached to a string hanging over a pulley (to left of post) and wound around a disk of mass M and radius R. This provides a force F = mg and a torque T = mgR, creating both linear acceleration a=F/M and angular acceleration a=T/I of the disk, where the moment of inertia of the disk I=MR^2/2, assuming that m is much smaller than M. The distance d and the rotation Q which the disk undergoes when released from rest can then be calculated: d=at^2/2=mgt^2/2M and Q=at^2/2=mgt^2/MR. Eliminating t, we obtain the relation between the linear and angular acceleration of the disc, which can easily be experimentally verified: Q=2d/R.

Note: The air table is only available in rooms 1410, 1412, and 0405 because it will not fit through a standard door.

An aluminum plate is used as a pendulum which can oscillate about either of the three principal axes. The moments of inertia are: I(x)=mb^2/3, I(y)=ma^2/3, and I(z)=I(x)+I(y)=m(a^2+b^2)/3, where a is the shorter side of the plate and b is the longer side. For this demonstration m=374g, a=20cm, and b=28.2cm.

A subject sits on the stool, with his or her arms extended, holding the weights. After the system is set into rotation, the subject pulls the weights in to his or her chest, decreasing the moment of inertia of the system and thus increasing the angular speed of the system.

Rotation of the large weighted propeller by a person sitting in the rotating chair causes rotation of the chair in the direction opposite to the direction the propeller is rotated, as demonstrated very effectively by Gwen in the photographs above.

At the bottom of the swing, the pumper raises herself by pulling quickly backward on the ropes. At that point there is no applied external torque, so conservation of angular momentum applies, and mv(1)r(1)=mv(2)r(2), where (1) refers to before the pull and (2) refers to after the pull. Pulling backward on the ropes raises the pumper, decreasing the radius with respect to thesupport point, and thus increasing her velocity. By conservation of energy the pumper thus rises to a higher level with each pump.

This analysis is perhaps somewhat of an oversimplification, but may be adequate for the beginner. See some of the references for a more complete and mathematically detailed description. This can only be done with a small subject using the fork truck swing.

A mass (the swing) hangs from a rope that passes over a pulley and is connected to the support post. A second shorter rope hangs freely from the horizontal section of the main rope.

Start the pendulum mass oscillating with a small amplitude. When the pendulum gets to its lowest position, pull gently down on the shorter rope, shortening the pendulum and thereby increasing its velocity. Release the rope as the pendulum nears its high point.

According to a possibly oversimplified analysis, conservation of angular momentum at the low point, before and after the pull is applied, explains why this procedure causes the amplitude of the swing to increase with time. See also discussion of parametric resonance.

A string about one meter long has a (relatively heavy) set of keys on one end and a (very light) match box on the other end. The string passes over a pencil with the keys hanging down and the matchbox held horizontal to the pencil with about two/thirds of the string between the pencil and the matchbox.

Q: What will happen when the match box is released?

A: Surprisingly, the keys will not fall to the floor. When the matchbox falls it develops angular momentum. Conservation of angular momentum of the matchbox causes it to rotate very rapidly about the pencil as the string pulls it in. Before the string is used up, the matchbox string actually wraps around the pencil, preventing the keys from falling onto the floor!

A rope is tied to a tennis ball at one end, and to a brick at the other. The rope runs loosely through a plastic handle, allowing it to slide freely.

Spin the ball on its rope around in a circle above your head. As the radius of rotation increases, the centripetal acceleration does as well, increasing the force acting on the brick. At a certain point, the force will be sufficient to lift the brick off the table!

Check out further discussion of this demonstration, and a full mathematical treatment, at the link below!

Show how linear and angular momentum are transferred between a small puck and the rectangular bar when the puck strikes the bar at various points along its length and/or at varying angles. Inelastic collisions can also be demonstrated using a puck with a velcro collar.