Chapter 10 - Friday October 22nd

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Presentation transcript:

Chapter 10 - Friday October 22nd Class 25 - Rotation Chapter 10 - Friday October 22nd Review Definitions, angular to linear conversions, kinetic energy Calculating rotational inertia Newton's second law for rotation Work, power and rotational kinetic energy Sample problems Reading: pages 241 thru 263 (chapter 10) in HRW Read and understand the sample problems Assigned problems from chapter 10 (due Sunday October 31st at 11pm): 2, 10, 28, 30, 36, 44, 48, 54, 58, 64, 78, 124

Review of rotational variables (scalar notation) Angular position: Angular displacement: Average angular velocity: Instantaneous angular velocity: Average angular acceleration: Instantaneous angular acceleration:

Relationships between linear and angular variables Position: Velocity: Time period for rotation: Tangential acceleration: Centripetal acceleration:

Kinetic energy of rotation where mi is the mass of the ith particle and vi is its speed. Re-writing this: The quantity in parentheses tells us how mass is distributed about the axis of rotation. We call this quantity the rotational inertia (or moment of inertia) I of the body with respect to the axis of rotation.

Calculating rotational inertia For a rigid system of discrete objects: Therefore, for a continuous rigid object: Finding the moments of inertia for various shapes becomes an exercise in volume integration. You will not have to do such calculations. However, you will need to know how to calculate the moment of inertia of rigid systems of point masses. You will be given the moments of inertia for various shapes.

Some rotational inertia

Parallel axis theorem If you know the moment of inertia of an object about an axis though its center of mass (c.o.m.), then it is trivial to calculate the moment of inertia of this abject about any parallel axis: Here, Icom is the moment of inertia about an axis through the center of mass, and M is the total mass of the rigid object. It is essential that these axes are parallel; as you can see from table 11-2, the moments of inertia can be different for different axes.