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.
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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.
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.
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.
If no net external work acts on a system, its total mechanical energy (kinetic plus potential) remains constant.
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
What does the work-energy theorem state about net work and kinetic energy?
How do you express rotational kinetic energy in terms of moment of inertia and angular velocity?
How would you calculate work done by a constant force at an angle?
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.