1. Parallel-Axis Theorem Pre-Lab Axis through the center of mass Rotational Inertia of a slab about a perpendicular axis through its center of mass

2. Parallel-Axis Theorem Pre-Lab Where M = mass of the slab a = width of the slab b = length of the slab Rotational Inertia of a slab about a perpendicular axis through its center But the density of the disk is constant. Hence, Also,

3. Parallel-Axis Theorem Pre-Lab Rotational Inertia of a slab about a perpendicular axis through its center Take the integral with respect to x with constant y

4. Parallel-Axis Theorem Pre-Lab Rotational Inertia of a slab about a perpendicular axis through its center Where M = mass of the slab a = width of the slab b = length of the slab Take the integral with respect to y with constant x

5. Parallel-Axis Theorem Pre-Lab Purpose:To calculate graphical and mathematical representations of the relationship between the rotational inertia of a body of mass M around a parallel axis of rotation not through the center of mass and the distance h from the center of mass to that parallel axis. Axis through the center of mass Parallel Axis

6. The clamp-on Super Pulley must be adjusted at an angle, so that the thread runs in a line tangent to the point where it leaves the 3-step Pulley and straight down the middle of the groove on the clamp-on Super Pulley (Figure 1.2). Parallel-Axis Theorem Pre-Lab

7. Since the masses are accelerating downward. Since the string doesn’t slip, the linear acceleration of the masses is equal to the tangential acceleration of the outside of the pulley. Parallel-Axis Theorem Pre-Lab

8. Newton’s Second Law Experimental Rotational Inertia about a parallel axis a perpendicular distance h from the center of mass Parallel-Axis Theorem Pre-Lab