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PHYS 218 sec. 517-520

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PHYS 218sec. 517-520

Review

Chap. 9

Rotation of Rigid Bodies

- 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.

Angular velocity

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
- How the body’s mass is distributed in space,
- 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 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.

Ex 9.8

Unwinding cable I

2m

final

initial

Ex 9.9

Unwinding cable II

Kinetic energy of m

Rotational kinetic energy of M;

I=MR2/2, w=v/R

initial

final