Four rods are included: The first set (taken from the demonstration B1-17: CENTER OF MASS - STICKS) includes a uniform wooden rod and a second rod with a weight at one end. The second set are two rods with the same mass, one weighted at the center and one weighted at both ends.

The student is asked to determine the difference between the rods. The difference between the first set is readily apparent, but determining the difference between the second set requires some experimenting. One way to "feel" the difference between the two latter rods is to hold each at the center and rotate your wrist back and forth. The large moment of inertia of the rod with weighted ends makes rotation of your wrist rather difficult compared with the rod weighted at the center.

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.

This demonstration can be used to introduce the Parallel Axis Theorem.

Please take care when using this device, especially when accelerating. You can gain a significant increase in rotational speed, so hold on! And it is best not to have a person push the chair around very much, as it is very easy to hit them with a weight by accident.

Engagement Suggestions

Background

To show this in a different way, a single user with a single weight can move themself in a circle by swinging their arm wide holding the weight from front to back, then drawing it inwards before extending their arm forwards again and repeating the motion. This is essentially a rotational analogue of pumping a swing.

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.

Sit on the chair (chair not rotating) with the wheel spinning and its axis oriented vertically. Reverse the angular momentum vector of the wheel by inverting the wheel, thus causing the entire chair to rotate in the original direction of the wheel rotation. Returning the wheel to its initial orientation causes the chair to cease its rotation.

Because the friction in the bearing of the rotating chair is very low, several cycles of this procedure can usually be completed before the system loses its energy and stops.

Engagement Suggestions

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.

You (or a student) can stand on the platform and rotate with minimal friction. The rotating platform can also be used with hand weights to study rotational inertia, conservation of angular momentum, and action-reaction.