What You’ll Do

1. Measure the moment of inertia of different objects by seeing how fast they roll down a ramp, compare to values calculated from objects’ shape and mass
2. Compare the initial potential energy and final kinetic energy of objects rolled down the ramp

Tools/Resources:

• Slanted cart track
• Meter stick, ruler, digital calipers
• Electronic scale
• Phone or digital camera
  • Fast Shutter Mode for Motion Capture with Casio Exilim Camera
• Tracker Software
  • Tracker Quick Start

Background

In earlier experiments you studied objects moving on a slanted track. In that case, you only had to account for the component of the force of gravity acting along the ramp. In this experiment the objects you study will be rolling (as opposed to carts sliding on wheels of negligible mass), so there will also be a static frictional force providing a torque of \tau=f_s\times R = I\alpha = Ia/R

The total acceleration will thus be a=\frac{g\sin\theta}{1+(I/mR^2)}

If the acceleration of a rolling object is measured and compared to the expected acceleration for an object sliding down the ramp without friction, the moment of inertia can be shown to be I=\left[ \frac{g\sin\theta}{a}-1 \right]mR^2

Also, because the objects will be rolling, their kinetic energy at the bottom of the track will be a combination of translational and rotational forms. mgh=\tfrac{1}{2}mv^2+\tfrac{1}{2}I\omega^2