Summary
Highlights
Linear momentum (p) equals mass times velocity. Angular momentum (L) for a particle is r cross p, and for a rigid object, it's moment of inertia times angular velocity. All are vector quantities.
Displacement is defined as the change in position. For linear motion, common symbols are X, Y, Z, or R. For angular motion, the symbol is Theta. Both linear and angular displacement are vector quantities.
Average velocity is calculated as change in position over change in time, while instantaneous velocity is the derivative of position with respect to time. Velocity is a vector. Angular velocity is denoted by the lowercase Omega.
Acceleration equations are similar to velocity equations, replacing position with velocity. Acceleration is a vector. Angular acceleration is symbolized by Alpha, also known as 'fishy thing' by some.
The video presents the four UAM equations in a slightly modified form for easier use. The UAAM equations follow the same form as the UAM equations, substituting linear terms with their angular counterparts.
There is no general linear equation for mass. However, rotational mass is called Moment of Inertia (symbolized by I). For a system of particles, it's the sum of mass times r-squared. For a rigid object, it's the integral of r-squared with respect to mass.
Linear (translational) kinetic energy is one-half mass times velocity squared. Rotational kinetic energy is one-half moment of inertia times angular velocity squared.
Newton's Second Law states that net force equals mass times acceleration, and also the derivative of momentum with respect to time. In rotational terms, net torque equals moment of inertia times angular acceleration, and also the derivative of angular momentum with respect to time. Force, acceleration, torque, and angular momentum are all vectors.
There is no single general equation for force, but equations exist for specific forces like gravity and friction. Torque is defined as the cross product of the position vector 'r' and force 'F' (r x F), where 'r' is from the axis of rotation to the force's application.
Linear power is the derivative of work with respect to time, or the dot product of force and velocity. Rotational power is the derivative of work with respect to time, or the dot product of torque and angular velocity.