This page gives a summary of important equations in classical mechanics.
Nomenclature
- a = acceleration (m/s^{2})
- F = force (N = kg m/s^{2})
- KE = kinetic energy (J = kg m^{2}/s^{2})
- m = mass (kg)
- p = momentum (kg m/s)
- s = position (m)
- t = time (s)
- v = velocity (m/s)
- v_{0} = velocity at time t=0
- W = work (J = kg m^{2}/s^{2})
- s(t) = position at time t
- s_{0} = position at time t=0
- r_{unit} = unit vector pointing from the origin in polar coordinates
- θ_{unit} = unit vector pointing in the direction of increasing values of theta in polor coordinates
Defining Equations
Center of Mass
where is the number of mass particles.Or in the continuous case:
Velocity
Acceleration
- a_{average} = Δv/Δt
- a = dv/dt = d^{2}s/dt^{2}
- Centripetal Acceleration
Momentum
Force
- ∑F = dp/dt = d(mv)/dt
- ∑F = ma (Constant Mass)
Impulse
- J = Δp = ∫Fdt
- J = FΔt if F is constant
Moment of Intertia
For a single axis of rotation:
Angular Momentum
Vector form:
- L = r×p = Iω
r is the radius vector
Torque
if |r| and the sine of the angle between r and p remains constant.- ∑τ = Iα
Precession
Energy
- ΔKE = ∫F_{net}·ds
- KE = ∫v·dp = 1/2 mv^{2} if m is constant
- PE_{due to gravity} = mgh (near the earth's surface)
Central Force Motion
Useful derived equations
Position of an accelerating body
Equation for velocity
- v^{2}=v_{0}^{2} + 2a·Δs