Work Energy Theorem
Work Energy Theorem - Related Videos
01:41
Work-energy Theorem
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2026
According to Newton’s second law of motion, the sum of all the forces acting on a particle (net force) determines the rate of change in the momentum of the particle (motion). Therefore, we should consider the work done by all forces acting on a particle, or the net work, to see its effect on the particle’s motion. The work-energy theorem equates work done by all the forces on an object to the change in its kinetic energy. The theorem can be used to calculate work done by a force when...
01:11
Work-Energy Theorem for Rotational Motion
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2025
The work-energy theorem for rotational motion is analogous to the work-energy theorem in translational motion. It states that the net work done by an external force to rotate a rigid body equals the change in the object's rotational kinetic energy. The power delivered is simply the time derivative of the work done; therefore, power is the dot product of torque and angular velocity. This relation is analogous to power in translational motion, which is given by the dot product of force and...
01:09
Work-Energy Theorem for Motion Along a Curve
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2023
The work-energy theorem can be generalized to the motion of a particle along any curved path. The simple argument here is that the curved path can be considered a sum of many infinitesimal paths, each of which is a straight path. The force on the particle can be considered constant along any such infinitesimal path so that the work-energy theorem can be applied along it. So, it is also valid for the sum of these paths. The net work done is the integral of the work done along the infinitesimal...
01:26
The Mean Value Theorem
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2026
The Mean Value Theorem establishes a fundamental connection between the overall change in a quantity and its change at a specific instant. It formalizes the idea that average change over an interval must be reflected by instantaneous change at some point within that interval. When a function behaves smoothly across a range, the theorem guarantees that this connection always exists.This relationship is captured mathematically by the Mean Value Theorem, as stated below.The meaning of this result...
08:52
Energy and Work
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2023
Source: Ketron Mitchell-Wynne, PhD, Asantha Cooray, PhD, Department of Physics & Astronomy, School of Physical Sciences, University of California, Irvine, CA This experiment demonstrates the work-energy principle. Energy is one of the most important concepts in science and is not simple to define. This experiment will deal with two different kinds of energy: gravitational potential energy and translational kinetic energy. Gravitational potential energy is defined as the energy an object...
FAQs
Displacement determines which part of a force transfers energy during motion. The component parallel to the displacement contributes work, while a perpendicular component does not increase or decrease the object’s kinetic energy through that displacement. This distinction helps isolate the force effect that changes speed and prevents unrelated force directions from being included in the energy calculation.
Positive work transfers energy to the object and increases its kinetic energy, whereas negative work removes kinetic energy. The sign depends on the force component’s direction relative to displacement. Applied forces may speed an object up, while opposing forces such as friction can reduce its speed. Evaluating the net sign predicts whether kinetic energy rises or falls.
The theorem remains useful when force changes during the motion because it connects the total work over the displacement with the overall change in kinetic energy. Instead of requiring a single constant force value, the analysis accounts for the force’s effect along the path. This makes the approach suitable for motions involving nonuniform applied forces.
First identify the object and its initial and final states, then determine the forces that perform work during the displacement. Resolve each force according to its component along the motion, assign the appropriate sign, and combine the contributions to obtain net work. Finally, set that result equal to the change in kinetic energy and solve for the requested quantity.
Each force contributes according to how it acts through the object’s displacement. Gravity can transfer energy as the object moves, friction generally removes kinetic energy when it opposes motion, and an applied force can either add or remove energy depending on direction. Separating these contributions clarifies which interactions control the final speed or kinetic-energy change.
The Work Energy Theorem is especially useful when the main information concerns force, displacement, mass, and speed rather than acceleration and elapsed time. It can simplify problems involving gravity, friction, applied forces, or changing force conditions by avoiding a direct time-based motion analysis. In mechanics, this provides an alternative route for determining motion outcomes.