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PHYS 218 sec. 517-520

PHYS 218 sec. 517-520. 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.

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PHYS 218 sec. 517-520

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

  2. 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.

  3. Analog between translation and rotation motion

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

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

  6. Polar coordinate system Therefore, this is valid in general.

  7. Polar coordinate system

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

  9. 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

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

  11. Ex 9.8 Unwinding cable I 2m final initial

  12. Ex 9.9 Unwinding cable II Kinetic energy of m Rotational kinetic energy of M; I=MR2/2, w=v/R initial final

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