Key Terms
Angular velocity (omega)
Rate of change of angle with time
Angular acceleration (alpha)
Rate of change of angular velocity
Tangential (linear) acceleration
At = r * alpha
Centripetal acceleration
Changes DIRECTION of velocity, not magnitude
Torque (tau)
The rotational analog of force; the "turning effectiveness" of a force
Moment of inertia (I)
Rotational analog of mass; resistance to change in rotation
Rotational kinetic energy
KE-rot = (1/2) * I * omega^2 (analogous to KE-trans = (1/2) * m * v^2)
Rotational work
W = tau * theta (analogous to W = F * d)
ROLLING WITHOUT SLIPPING
Connects linear and rotational motion through v = r * omega. This relationship lets you substitute one for the other and
SOUP CAN RULE
Thicker fluid rotates with the can and increases I-effective, stealing more PE for rotation and slowing the can down. Th
Angular momentum (L)
Rotational analog of linear momentum
Relationship between torque and angular momentum
Tau-net = delta-L / delta-t (analogous to F-net = delta-p / delta-t)
PERCUSSION POINT (sweet spot)
When an extended object is struck, there is one specific point where the strike produces no reaction force at the pivot.
Right-hand rule
Curl the fingers of your right hand in the direction of rotation. Your thumb points in the direction of both omega and L
If the gyroscope is NOT spinning
It simply falls over in the direction of the torque, as expected.