Work-energy theorem

Definition

The work-energy theorem states that the net work done by forces on an object is equal to the change in its kinetic energy. It is a fundamental principle connecting the concepts of work and energy.

5 Must Know Facts For Your Next Test

1. The mathematical expression for the work-energy theorem is $W_{\text{net}} = \Delta KE = KE_f - KE_i$, where $W_{\text{net}}$ is the net work, $KE_f$ is the final kinetic energy, and $KE_i$ is the initial kinetic energy.
2. In rotational motion, the work-energy theorem can be applied using rotational kinetic energy, represented as $\frac{1}{2} I \omega^2$, where $I$ is the moment of inertia and $\omega$ is the angular velocity.
3. The work done by a constant force can be calculated using $W = Fd \cos(\theta)$, where $F$ is the force, $d$ is the displacement, and $\theta$ is the angle between the force and displacement vectors.
4. If no net external work acts on a system, its total mechanical energy (kinetic plus potential) remains constant.
5. In real-world scenarios, non-conservative forces like friction often cause some of the mechanical energy to transform into other forms of energy like heat.

Review Questions

Related terms

Kinetic Energy:

Energy possessed by an object due to its motion, given by $KE = \frac{1}{2} mv^2$, where $m$ is mass and $v$ is velocity.

Potential Energy:

Energy stored in an object due to its position or configuration. Gravitational potential energy near Earth's surface is given by $PE = mgh$, where $m$ is mass, $g$ is gravitational acceleration, and $h$ is height.

Moment of Inertia:

A measure of an object's resistance to changes in its rotation rate. It depends on both mass distribution relative to the axis of rotation.