10.3 Dynamics of rotational motion: rotational inertia  (Page 3/9)

Take-home experiment

Cut out a circle that has about a 10 cm radius from stiff cardboard. Near the edge of the circle, write numbers 1 to 12 like hours on a clock face. Position the circle so that it can rotate freely about a horizontal axis through its center, like a wheel. (You could loosely nail the circle to a wall.) Hold the circle stationary and with the number 12 positioned at the top, attach a lump of blue putty (sticky material used for fixing posters to walls) at the number 3. How large does the lump need to be to just rotate the circle? Describe how you can change the moment of inertia of the circle. How does this change affect the amount of blue putty needed at the number 3 to just rotate the circle? Change the circle's moment of inertia and then try rotating the circle by using different amounts of blue putty. Repeat this process several times.

In what direction did the circle rotate when you added putty at the number 3 (clockwise or counterclockwise)? In which of these directions was the resulting angular velocity? Was the angular velocity constant? What can we say about the direction (clockwise or counterclockwise) of the angular acceleration? How could you change the placement of the putty to create angular velocity in the opposite direction?

Problem-solving strategy for rotational dynamics

1. Examine the situation to determine that torque and mass are involved in the rotation . Draw a careful sketch of the situation.
2. Determine the system of interest .
3. Draw a free body diagram . That is, draw and label all external forces acting on the system of interest.
4. Apply $\mathrm{net\; \tau }=\mathrm{I\alpha }\mathrm{, }\alpha =\frac{\text{net τ}}{I}$ , the rotational equivalent of Newton's second law, to solve the problem . Care must be taken to use the correct moment of inertia and to consider the torque about the point of rotation.
5. As always, check the solution to see if it is reasonable .

Making connections

In statics, the net torque is zero, and there is no angular acceleration. In rotational motion, net torque is the cause of angular acceleration, exactly as in Newton's second law of motion for rotation.