0.32 Phy1320: angular momentum -- the mathematics of torque  (Page 11/13)

Imagine that this is the puck mentioned above that is constrained to move in a circle. Label this point P.

A radial line from the center

Use a pipe cleaner or a rubber band to draw a line from the puck to the center of the circle. Label this line r.

Create a force vector

Make a little loop at one end of a pipe cleaner that is about half the radius of your circle and place the loop around the pushpin that represents the puck atP.

Leave it loose enough that it can be rotated around the pin. Imagine that this is a vector that describes a force being applied to the puck with the tailof the vector at the puck.

Point the force vector at the center

Begin by pointing the force vector directly at the center of the circle. You will probably be able to imagine that since the puck is not free to movedirectly to the center, a force in this direction will not cause the puck to move.

The technical reason that it won't cause the puck to move is because the force doesn't have a component that is tangent to the circle at the locationof the puck.

Rotate the force vector

Now rotate the force vector clockwise by about 30 or 40 degrees and pin it down so that it won't move. Label the tip of the force vector F.

Draw the tangential component of the force vector

This may be the most difficult part of this exercise for a blind student. Use your protractor (or some other method that you know about) to find a point on the line labeled r such that a linethrough that point and perpendicular to r goes through the tip of the force vector. Mark that pointwith a pushpin and label it Q.

Draw a line from Q to F

Use a pipe cleaner to draw a line from Q to F. That line represents the component of the force vector that is tangent to the circle at the locationof the puck. (Actually it is parallel to the tangential component of the force vector, but that is OK. It is still the correct length and points in the correctdirection.) The direction of that tangential force component is from Q to F.

This is the component of the force vector that causes the puck to move. Label this vector Ft for tangential force.

The radial component of force

Use a pipe cleaner to draw a line from P to Q. This is the component of the force vector that points directly from the puck to the center of the circle. Thiscomponent won't cause the puck to move.

A right triangle

If you examine your vector diagram at this point, you can determine that the points labeled P, Q, and F represent the vertices of a right triangle, with theright angle at the point Q.

The length of the tangential force vector

Label the interior angle at P with an A. Now you should be able to determine that the length of the tangential vector named Ft is equal to the product of the force F and thesine of the angle A.

Ft = F*sin(A)

where

• F is the force vector.
• Ft is the component of the force vector that is tangent to the circle at the location of the puck. This force is also perpendicular to the line fromthe puck to the center of the circle.
• A is the angle that the force vector makes with the line r.