# Potential & Kinetic Energy

Potential energy is stored energy. There are different types of potential energy situations that can be applied to a rigid body. As with a particle, the potential energy of holding a rigid body at a certain height can be applied, along with the potential energy of a compressed spring. Refer to equations 1-2.

(Eq 1)  $V_y=-WΔy$

W = Weight

Δy = Height object is being held at

Vy = Potential energy of hanging mass

(Eq 2)  $V_s=\frac{1}{2}kΔs^2$

k = spring constant

Δs = Amount spring is compressed

Vs = Potential energy of a spring

An additional potential energy situation that can be considered when dealing with a rigid body is called the work of a couple. The work of a couple takes in consideration of rotational motion. It considers the moment placed on the rigid body, and the angular displacement of that rotation. Refer to equation 3.

(Eq 3)  $V_M=M(θ_2-θ_1)$

M = Moment

2 – θ1) = deflected angle

VM = Potential Energy of a couple

## Kinetic Energy

Kinetic energy is energy that is being used, and relates directly to motion . As with a particle, kinetic energy for translational motion of a rigid body is represented by equation 4. However, for rotation about a fixed axis, kinetic energy is represented by equation 5, which takes in consideration of the mass moment of inertia and the angular velocity.

(Eq 4)  $T=\frac{1}{2}mv^2$

m = mass

v = velocity

(Eq 5)  $T=\frac{1}{2}Iϖ^2$

I = Mass Moment of Inertia

ϖ = angular velocity