Note that there are three arms over which weights may be hung, and thus a maximum of three vectors can be summed.

A rigid scale is attached to the torsional chair (with its internal coil spring attached to provide a countering force). An arbitrary force (measured by the spring scale) can be exerted at an arbitrary angle (measured by the protractor) at an arbitrary distance from the center of the chair (measured by the scale) to produce some arbitrary rotation of the chair against its restoring spring. Equal torques can be applied in several different ways, or torques can be scaled by changing one or more of the variables. Measurements are good to about ten percent.

The photographs above show the chair being rotated about 180 degrees by an external torque, which is created by a force perpendicular to the radius vector (center) or at an angle of 45 gegrees with respect to the radius vector (right).

Note that this demonstration and demonstrations B2-22 and B2-32 use many of the same components.

Two wheel and axle assemblies are provided. For each, there are cylinders of smaller radius r and larger radius R. A smaller weight m is suspended from a string wrapped around the larger radius R, and a larger weight M suspended from the smaller radius r. For equilibrium of torques:

Weights are hung at points along a 50cm scale to balance torques about the pivot at the center of the scale.

A bracket is bent into a right triangle with arms of length a and 2a, and suspended from the end of the small arm as photographed. What is the angle of repose r of the small arm with the vertical, at equilibrium?

From the equation of torques, w1 x1 = w2 x2,

where: w1= mg and x1= a/2 sin r,

also: w2 = 2mg and x2 = a cos r - a sin r)

From these, tan r = 4/5, and r = 38.66 degrees.

Balance the meter stick on your two index fingers, with one finger initially at one end and the other finger about one-quarter of the way from the other end. Slide your fingers together (moving either one or the other or both). Your fingers will always end up together directly under the center of mass.

Try different starting points. Try adding a 100 gram weight onto either end. Try greasing your finger. It always works. Ask your students what they think will happen before doing the original experiment. Ask them again after adding a weight to one end.

Balance the meter stick ASYMMETRICALLY on the two rotators, and start the rotators in motion. Then balance the meter stick as close to SYMMETRICALLY as you can and start the rotators. It will always fall off if the rotators rotate outward, and will always end up balanced with the CM in the center if the rotators rotate inward. Which direction it moves depends on very small asymmetries!! Click the links below for several cases:

Rotators rotate inward, meter stick starts asymmetrically balanced.

Rotators rotate outward, meter stick starts asymmetrically balanced.

Rotators rotate outward, meter stick starts symmetrically balanced and falls to the left.

Rotators rotate outward, meter stick starts symmetrically balanced and falls to the right.

Try different starting points. Try adding a 100 gram weight onto either end. (Please ask for the weight so we do not overlook it.) It always works. Ask your students what they think will happen before doing the original experiment. Ask them again after adding a weight to one side.

Photograph at the top shows arm model in neutral force configuration

Force applied by the biceps (lower left), pulling up with the hand: Apply 2.5 kg to the biceps cable to support the unloaded forearm. The forearm may be kept at equilibrium by the simultaneous addition of masses in the ratio of 10:1 at the biceps and at the hand. The torques are balanced almost independently of the angular position of the arm.

Force applied to the triceps (lower right), pushing down with the hand: Hang the spring scale between the top hook and the hand hook, and attach the hanger to the triceps cable. Add masses to the hanger to determine how much force in the triceps is necessary to push down with the force read on the scale.

Referring to the three photographs above:

First class lever (top): the pivot is between the load and the applied force (push down with hand or pull down with spring scale at left in photo).

Second class lever (lower left): the load is between the pivot and the applied force.

Third class lever (lower right): the applied force is between the load and the pivot.