review #1 -  · 9/17/07 physics 102.002 review #1 2 motion. 9/17/07 physics 102.002 review #1 3...

Review #1

Physics 102.002September 17, 2007Prof. Michael Gold

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Motion

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Newton’s Laws

Newton (I) II: inertial mass, force,

Newton III: interaction between two objects,

force of 1 on 2

is equal and opposite to

force of 2 on 1

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Newtonian Gravity

Universal Law:

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Kepler’s Laws

3. Period and semi-major axis

2. Motion along ellipse “equal areasin equal times” (conservation ofangular momentum)

1. Planets move in elliptical orbitswith sun at one focus

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Kinetic Energy and Work

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Momentum

Equivalent to Newton III

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Mechanical EnergyPotential Energy defined for conservative force:

Examples: Gravity, (ideal) spring

Counter Example: friction

Near earth’s surface

For (ideal) spring (k measures springstrength

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Conservation of MechanicalEnergy

If only conservative forcesare present,

E = T + UIs conserved. Sum of kineticand potential energy doesnot change.

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Angular Momentum

Moment of inertia I defined as

Sum of mass x (distance to rotation axis)2

Angular momentum is product of moment ofinertia and angular speed

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Rotational Kinetic Energy

Note similarity between linear andangular momentum, kinetic energy

Mass => moment of inertia

Speed => angular speed

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Work Example: part ICentripetal force does no workbecause force is perpendicular todisplacement

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Work example part IIWhile spiraling in velocity isnot perpendicular to force

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Algebra

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Simple Harmonic Motion

For spring or simple pendulum,Force prop-to displacementU = 1/2 (const) (displacement)2

Sketch ofU (parabola)

E

displacement

Turningpoints