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Inertia, Linear Velocity and Acceleration, Force, Newton's Laws, Falling Objects, Projectile Motion, Energy and Work, Gravitational Potential Energy

Equations:

speed (v) = distance / time = d/t
acceleration (a) = change in velocity / time = D v/t
Force (F) = mass x acceleration = m a
Weight = mass x gravitational acceleration = mg

If an object starts out at position x₀ and velocity v₀, and accelerates at a constant acceleration a for time t, its final velocity will be
v_f = v₀ + at
and its final position will be
x_f = v₀t + at²/2

Work = Force x distance = F d
Gravitational acceleration on Earth = g = 9.80 m/s²
Gravitational Potential Energy (PE) = mgh

Energy is conserved in any isolated system, but can change form. Forms of energy include potential energy, kinetic energy, and heat. If a force acts on a system, the change in its energy is equal to the work done by the force. If the energy increases, positive work is done on the system. Only the component of force along the direction of motion contributes to the work done.

The amount of force needed to push an object of weight mg up a ramp of length L and height h is mg h/L. The factor h/L is the mechanical advantage of the ramp.

Remember that position, velocity, acceleration, and force are all represented by vectors: they have a magnitude and direction. Velocity is a vector, but speed, its magnitude, is not.

Units:

The SI unit of time is the second (s).
The SI unit of distance is the meter (m).
The SI unit of velocity is meters per second (m/s).
The SI unit of acceleration is meters per second per second (m/s²).
The SI unit of mass is the kilogram (kg).
The SI unit of force is the Newton (N). 1 N = 1 kg m/s².
The SI unit of work or energy is the Joule (J). 1 J = 1 N m.

Rotational Motion, Angular Velocity and Acceleration, Torque, Moment of Inertia, Center of Mass, Friction, Power, Momentum and Angular Momentum, Impulse, Kinetic Energy

Equations:

Angular velocity (w) = change in angle / time = D q / t
Angular acceleration(a) = change in angular velocity / time = D w / t
Torque = length of lever arm x perpendicular force = r F_perp.
Torque = moment of inertia x angular acceleration = I a
Power = Work/Time
Momentum (p) = mass x velocity = m v
Change in Momentum = Impulse = Force x Time = F t
Angular Momentum (L) = Moment of Inertia x angular velocity = I w
Alternatively, L = length of lever arm x perpendicular momentum = r p_perp.
Translational Kinetic Energy = m v²/2
Rotational Kinetic Energy = Iw²/2

Friction acts in a direction opposing motion. It is proportional to how much force is pushing two objects together. Static friction (before something starts moving) is greater than kinetic friction (while something is moving). Friction converts mechanical energy into thermal energy.

Both momentum and angular momentum are conserved in any isolated system. Any change in these is called the impulse or angular impulse, and is due to an external force or torque acting on the system for some time.

An object's moment of inertia is proportional to its mass, but depends on its shape and position relative to the rotation axis. The further the mass is from the rotation axis, the greater the moment of inertia. A hollow ball has a greater moment of inertia about its central axis than a solid ball of the same mass. A rod has a greater moment of inertia about a pivot point at its end than it would about a pivot point at its center.

Units:

The SI unit of angle is the radian. There are 2p radians in a circle. The radian is often considered to be dimensionless, and not written explicitly.
The SI unit of angular velocity is radians per second, or simply s^-1 if the radians are not shown.
The SI unit of momentum is kg m/s, or N s.
The SI unit of moment of inertia is kg m².