Key Equations in General Kinematics and Dynamics

Displacement in linear motion Δx =

v0t + 1/2 at^2

Final velocity in linear motion v =

v0 + at

Final velocity squared in linear motion v^2 =

v0^2 + 2aΔx

Centripetal force Fc =

mv^2/r

Angular displacement θ =

s/r

Angular velocity ω =

Δθ/Δt

Force from Newton's 2nd law F =

ma

Gravitational force between two masses Fg =

Gm1m2/r^2

Gravitational potential energy PEg =

-Gm1m2/r

Kinetic energy KE =

1/2 mv^2

Work done by a force W =

Fd cos θ

Power P =

W/t = Fv

Momentum p =

mv

Impulse is

the change in momentum.

Impulse, J is impulse, J=

FΔt where F is force, and Δt is the time interval.

Conservation of Momentum

m1v1 + m2v2 = m1v1' + m2v2' where m1 and m2 are the masses of the objects, v1 and v2 are their initial velocities, and v1' and v2' are their final velocities.

Torque τ is torque, τ=

rFsinθ where r is the lever arm, F is the force, and θ is the angle between the force and the lever arm.

Angular Momentum L is angular momentum, L=

mvr where m is mass, v is velocity, and r is the distance from the axis of rotation.

Rotational Kinetic Energy KE_rot =

1/2 Iω^2 where * is rotational kinetic energy, I is the moment of inertia, and ω is angular velocity.

Moment of Inertia, I is the moment of inertia, I=

I is the moment of inertia, I=mr^2 where m is mass, and r is the distance from the axis of rotation.

Period of a Mass on a Spring T=

2π√(m/k) where * is the period, m is the mass, and k is the spring constant.

Frequency of a Mass on a Spring, f=

1/T=1/(2π)√(k/m) where * is frequency, T is the period, k is the spring constant, and m is the mass.

Period of a Simple Pendulum T=

2π√(L/g) where * is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

Fluid Pressure P=

P0+ρgh where * is the pressure at depth, P0 is the surface pressure, ρ is the fluid density, g is the acceleration due to gravity, and h is the depth.

Buoyant Force FB=

ρVg where * is the buoyant force, ρ is the fluid density, V is the volume of the displaced fluid, and g is acceleration due to gravity.

Continuity in Fluid Flow

A1v1=A2v2 where A1 and A2 are the cross-sectional areas, and v1 and v2 are the fluid velocities at points 1 and 2.