Types of Energy in Physics

Why This Matters

Energy is the currency of physics—every problem you'll encounter on the AP Physics 1 exam ultimately comes down to tracking how energy moves, transforms, and transfers between objects and systems. You're being tested on your ability to identify what type of energy a system has, how that energy changes when forces do work, and why energy is conserved (or appears not to be) in different scenarios. These concepts connect directly to Unit 3's focus on work and energy conservation, and they extend into Unit 6 when objects start rotating.

Don't just memorize the formulas for kinetic and potential energy—know when each type applies and how they transform into one another. The exam loves questions where you must track energy through a system: a ball rolling down a ramp, a spring launching a cart, or two objects colliding. Master the conceptual categories below, and you'll be ready to tackle any energy problem they throw at you.

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Energy of Motion

Objects in motion carry energy by virtue of that motion. The faster something moves or spins, the more kinetic energy it possesses. AP Physics 1 distinguishes between translational motion (moving through space) and rotational motion (spinning), and you need to account for both when analyzing rolling objects.

Translational Kinetic Energy

• Depends on mass and velocity squared—calculated as $K_{trans} = \frac{1}{2}mv^2$, so doubling speed quadruples the energy
• Applies to center-of-mass motion—even rotating objects have translational KE if their center of mass is moving
• Key for collision analysis—elastic collisions conserve this quantity, while inelastic collisions do not

Rotational Kinetic Energy

• Depends on moment of inertia and angular velocity—calculated as $K_{rot} = \frac{1}{2}I\omega^2$, where $I$ depends on mass distribution
• Must be included for rolling objects—a rolling ball has both translational and rotational kinetic energy
• Different shapes store rotation differently—a hoop ($I = MR^2$) has more rotational KE than a solid sphere ($I = \frac{2}{5}MR^2$) at the same $\omega$

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Stored Energy (Potential Energy)

Potential energy represents energy stored in a system due to position or configuration. This energy can be released and converted to kinetic energy when the system changes. The two main types you'll see are gravitational (position in a field) and elastic (deformation of a spring).

Gravitational Potential Energy

• Depends on height above a reference point—calculated as $U_g = mgh$, where you choose the zero level
• Only changes in height matter—the path taken doesn't affect $\Delta U_g$, only initial and final positions
• Converts to/from kinetic energy—a falling object trades gravitational PE for KE at a rate determined by $g$

Elastic Potential Energy

• Stored in deformed springs—calculated as $U_s = \frac{1}{2}kx^2$, where $x$ is displacement from equilibrium
• Quadratic relationship with displacement—compressing a spring twice as far stores four times the energy
• Ideal springs are conservative—all stored energy can be recovered as kinetic energy with no losses

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Total Mechanical Energy

Mechanical energy is the sum of all kinetic and potential energies in a system. In the absence of non-conservative forces like friction, mechanical energy is conserved. This principle is your most powerful problem-solving tool.

Mechanical Energy

• Sum of kinetic and potential energies—$E_{mech} = K + U$, including all forms present in the system
• Conserved in ideal systems—when only conservative forces (gravity, springs) do work, $E_{mech,i} = E_{mech,f}$
• Transforms but doesn't disappear—a pendulum continuously exchanges KE and PE while total $E_{mech}$ stays constant

Conservation of Energy

• Energy cannot be created or destroyed—it only transforms between forms or transfers between systems
• Applies universally—even when mechanical energy decreases, total energy (including thermal) is conserved
• Enables before/after analysis—set $E_i = E_f$ to solve for unknown speeds, heights, or compressions

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Energy Transfer Mechanisms

Energy doesn't just sit there—it moves between objects and changes forms. Work is the mechanism by which forces transfer energy, and power tells you how fast that transfer happens.

Work-Energy Theorem

• Work equals change in kinetic energy—expressed as $W_{net} = \Delta K$, connecting force and motion
• Net work from all forces—includes contributions from gravity, springs, friction, and applied forces
• Bridges force and energy approaches—use this when you know forces and want to find speed changes

Power

• Rate of energy transfer—calculated as $P = \frac{W}{t}$ or equivalently $P = Fv$ for constant force and velocity
• Measured in watts—one watt equals one joule per second ($1 \text{ W} = 1 \text{ J/s}$)
• Determines how quickly work gets done—two machines can do the same work, but the more powerful one does it faster

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Energy Dissipation and Efficiency

Real systems lose mechanical energy to friction and other non-conservative forces. This energy isn't destroyed—it becomes thermal energy—but it's no longer available for mechanical work.

Thermal Energy

• Kinetic energy of microscopic particles—increases when friction converts mechanical energy into heat
• Represents "lost" mechanical energy—in problems with friction, $\Delta E_{thermal} = f_k \cdot d$
• Cannot be fully recovered—once mechanical energy becomes thermal, it can't all be converted back

Efficiency

• Ratio of useful output to total input—calculated as $\text{Efficiency} = \frac{E_{out}}{E_{in}} \times 100\%$
• Always less than 100% in real systems—friction, air resistance, and other losses reduce useful output
• Quantifies energy losses—helps compare how well different machines convert energy to useful work

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Quick Reference Table

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Self-Check Questions

1. A solid sphere and a thin hoop of equal mass and radius roll down the same frictionless incline from rest. Which reaches the bottom with greater translational speed, and why?

2. Compare and contrast gravitational potential energy and elastic potential energy in terms of how each depends on displacement from equilibrium.

3. A block slides across a rough surface and comes to rest. Is mechanical energy conserved? Is total energy conserved? Explain what happens to the "missing" energy.

4. Two identical cars accelerate from rest to the same final speed. Car A takes 5 seconds; Car B takes 10 seconds. Compare the work done on each car and the power required for each.

5. In a perfectly inelastic collision, two objects stick together. What quantity is conserved, what quantity is not conserved, and where does the "lost" energy go?