Experiment 9: Rotational Dynamics
Translational motion, or motion without rotation, can be analyzed in terms of force, mass, acceleration, velocity, and momentum. Rotational motion is best studied in terms of a corresponding set of concepts. In order, these are torque, moment of inertia, angular acceleration, angular velocity, and angular momentum.
In some ways the study of rotational motion is similar to the study of translational motion, but a complete mathematical treatment of rotation is much more complicated. This is particularly true when it is necessary to ascribe vector properties to rotational motion. A number of demonstrations and experiments will be set up to illustrate the basics of rotational dynamics. The similarity to translational motion will be fairly obvious in a few parts of the lab. In others, the motion is complex and the goal of the lab is to describe the motion rather than give a complete physical and mathematical explanation. The procedure in lab is to observe and experience the demonstrations, think about them and answer the questions using diagrams and applicable laws of physics.
Part 1: TORQUE
Close a door by pushing on the doorknob. Close the door again using approximately the same force but applying it 5 centimeters away from the hinges. Try again by applying the force on the edge of the door in a direction pointing toward the hinges. Summarize and explain your observations. Comment on the difference between force and torque.
Part 2: CONSERVATION OF ANGULAR MOMENTUM
Part 3: SHAPE AND MOMENT OF INERTIA
A heavy mass in free fall does not fall faster than a light mass. The extra weight is compensated for by extra resistance. A heavy mass on a frictionless plane does not slide down faster than a light mass. A heavy ring and a light ring both roll down an inclined plane with the same speed. What about a ring and a disk? Try this with combinations of rings and disks of different masses. Describe the results and give an explanation. It may be helpful to write down an energy equation for the case of 2 rings of different radii and different masses. Also try the energy equation for a ring and a disk of the same radius and mass.
Part 4: CONSERVATION OF ANGULAR MOMENTUM (AGAIN)
Part 5: PRECESSION OF A SPINNING TOP (GROUP DEMONSTRATION)
This is an interesting phenomenon, and a very difficult one to explain. Both torque and angular momentum must be treated as vectors. Torque causes angular momentum to change according to the following equation:
To use this equation the direction of a torque vector must be defined. Follow the moment arm with the fingers of your right hand. Then turn your fingers to follow the force. As you do this, your thumb will point in the direction of the torque vector.
A bicycle wheel will be set up so that it can be suspended from a rope as it spins. What is the direction of the torque vector for the accompanying diagram?
Set the bicycle wheel spinning so that when viewed from the left in the diagram, it is spinning counterclockwise. Release the wheel. What happens? Show the direction of the angular momentum vector.