PHYS 218 sec. 517-520 Review Chap. 9 Rotation of Rigid Bodies.

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PHYS 218 sec Review Chap. 9 Rotation of Rigid Bodies

What you have to know Rotational kinematics (polar coordinate system) Relationship & analogy between translational and angular motions Moment of inertia Rotational kinetic energy Section 9.6 is not in the curriculum.

Analog between translation and rotation motion

Angular velocity and acceleration Angular velocity The angular velocity and angular acceleration are vectors. Follow the right hand rule.

Rotation with constant angular acceleration All the formulas obtained for constant linear acceleration are valid for the analog quantities to translational motion

Polar coordinate system Therefore, this is valid in general.

Polar coordinate system

Energy in rotational motion Rotational motion of a rigid body Depends on 1.How the body’s mass is distributed in space, 2.The axis of rotation

Moment of inertia Moments of inertia for various rigid bodies are given in section 9.6 Rotational kinetic energy is obtained by summing kinetic energies of each particles. Each particle satisfies Work- Energy theorem Work-Energy theorem holds true for rotational kinetic energy includes rotational kinetic energy

Parallel-axis theorem Moments of inertia depends on the axis of rotation. There is a simple relationship between I cm and I P if the two axes are parallel to each other. Two axes of rotation 1.If you know I CM, you can easily calculate I P. 2.I P is always larger than I CM. Therefore, I CM is smaller than any I P, and it is natural for a rigid body to rotate around an axis through its CM.

Ex 9.8 Unwinding cable I initial final 2m

Ex 9.9 Unwinding cable II initialfinal Kinetic energy of m Rotational kinetic energy of M; I=MR 2 /2,  =v/R

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