Physics (university) · Part 04
Rotation and gravity
Spinning objects, circular motion, orbits and the law of gravitation.
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- Angular velocityHow fast something turns, measured in radians per second. One full turn is 2 pi radians.
- Centripetal accelerationThe inward acceleration that keeps something on a circle, a = v squared / r. It changes direction, not speed.
- Centripetal forceThe net inward force needed for circular motion, F = m v squared / r. It is a role played by tension, friction or gravity.
- TorqueThe turning effect of a force, torque = r F sin theta. Longer lever arms need less force.
- Moment of inertiaHow hard an object is to spin. It depends on mass and how far the mass sits from the axis, I = sum of m r squared.
- Rotational second lawNet torque equals moment of inertia times angular acceleration, tau = I alpha. It is F = ma for spinning.
- Angular momentumRotational momentum, L = I omega. It stays constant when no outside torque acts.
- Universal gravitationEvery two masses attract with a force F = G M m / r squared, where G is 6.67e-11 in SI units.
- Orbital speedThe speed that keeps a satellite in circular orbit, v = sqrt(G M / r). Gravity supplies the centripetal force.
- Escape velocityThe launch speed needed to leave a planet and never fall back, v = sqrt(2 G M / R), ignoring air.
- Kepler's third lawThe square of a planet's orbital period is proportional to the cube of its average distance from the Sun.