Formula used
- From speed: KE = 1/2 m v^2
- From angular speed: v = omega*L, then KE = 1/2 m (omega*L)^2
- From vertical drop: KE = m*g*h and v = sqrt(2*g*h)
- From angles (simple pendulum): Delta h = L( cos(theta) - cos(theta0) ), so KE = m*g*Delta h
How to use this calculator
- Pick a calculation mode that matches your known values.
- Enter mass and confirm g for your location.
- Provide the required inputs for your mode (speed, angles, length, or height).
- Select the output unit for kinetic energy.
- Press Calculate to see results above the form.
- Use Download CSV or Download PDF to export.
Example data table
| Mode | Inputs | Output (KE) | Notes |
|---|---|---|---|
| From speed | m = 2.0 kg, v = 3.0 m/s | 9.0 J | Uses KE = 1/2 m v^2 |
| From angular speed | m = 1.5 kg, L = 1.2 m, omega = 2.5 rad/s | 8.44 J | v = omega*L = 3.0 m/s |
| From drop height | m = 1.0 kg, h = 0.50 m, g = 9.80665 | 4.90 J | Assumes no losses |
| From angles | m = 0.8 kg, L = 1.0 m, theta0 = 40 deg, theta = 0 deg | 1.96 J | KE at bottom from release |
Kinetic energy in a swinging pendulum
1) What this calculator measures
This calculator estimates a pendulum bob’s kinetic energy. It accepts mass, gravity, and a motion description (angles, speed, angular speed, or drop height). Results include kinetic energy in multiple units, computed linear speed, and the equivalent vertical drop that would create the same energy.
2) Angle mode and energy conservation
Angle mode assumes the bob is released from rest and losses are negligible. The height change comes from pendulum geometry: Δh = L(cosθ − cosθ₀), where L is the pivot-to-center length. Kinetic energy follows KE = m·g·Δh, and the maximum occurs near the bottom when θ is close to 0°.
3) Speed mode for measured velocity
If you measured bob speed with video tracking, a photogate, or a sensor, use speed mode. The tool applies KE = ½m v². Because velocity is squared, doubling v makes KE four times larger, so unit selection and measurements improve accuracy.
4) Angular speed mode with v = ωL
When you know angular speed, the calculator converts ω (rad/s, rpm, or deg/s) into linear speed using v = ωL. It then computes KE = ½m(ωL)². This mode is helpful for encoder readings or rotation counters when length is known.
5) Height mode as a quick estimate
Height mode uses the energy relationship KE = mgh, which is equivalent to converting potential energy into kinetic energy. It also reports v = √(2gh). For example, a 0.50 m drop at g ≈ 9.81 m/s² gives v ≈ 3.13 m/s and 4.90 J per kilogram of mass.
6) Practical ranges and data checks
Typical lab pendulums use L from 0.2–2.0 m and release angles from 5° to 60°. Large angles and long runs increase drag, so real kinetic energy can be lower than ideal predictions. If the current angle is above the release point, Δh becomes negative; the tool sets KE to zero to reflect an ideal swing that cannot exceed its starting energy.
7) Exports for labs and reporting
Download CSV to log multiple trials, compute averages, and plot energy versus angle or speed. Download PDF to share a clear summary with inputs, units, and outputs. Pair exports with notes about timing, damping, and measurement method for a complete lab report.
FAQs
1) Does the angle method include friction and air resistance?
No. Angle mode assumes ideal energy conversion. Real swings lose energy, so measured speed is usually lower than the ideal value, especially for long runs or large release angles.
2) What angle reference does the calculator use?
Angles are measured from the vertical line through the pivot. A bottom position is 0°. Positive or negative direction does not matter because the formulas use cosine.
3) Why can kinetic energy become zero in angle mode?
If the current angle is above the release angle, the height drop becomes negative. The calculator sets KE to zero because, in an ideal swing from rest, the bob cannot rise above its starting energy.
4) Which mode should I use for lab data?
Use speed mode if you have measured v from tracking or sensors. Use angle mode if you only know release and current angles and want an ideal estimate for comparison.
5) What length should I enter?
Enter the distance from the pivot point to the bob’s center of mass. Using the string length to the bob’s surface can slightly understate length and affect the angle-based height change.
6) Why does kinetic energy scale so strongly with speed?
Because KE = ½m v². A small increase in speed produces a larger increase in energy. For example, increasing speed by 10% increases kinetic energy by about 21%.