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Dynamics: 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.

Potential energy of a height (1)

W = Weight

Δy = Height object is being held at

Vy = Potential energy of hanging mass

Potential energy of a height

Potential energy of a spring (2)

k = spring constant

Δs = Amount spring is compressed

Vs = Potential energy of a spring

potential energy of a compressed 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.

potential energy of a couple (3)

M = Moment

2 - θ1) = deflected angle

VM = Potential Energy of a couple

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.

translational kinetic energy (4)

m = mass

v = velocity

rotational kinetic energy (5)

I = Mass Moment of Inertia

ω = angular velocity

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