Calculator Inputs
Formula Used
The calculator treats the push as a tangential force along the pendulum path.
- Weight: W = m × g
- Gravity tangential force: Fg = m × g × sin(θ)
- Acceleration force: Fa = m × L × α
- Applied force: F = Fg + Fa + friction
- Safe force: Fs = F × safety factor
- Pivot torque: τ = F × L
- Tension: T = m × g × cos(θ) + m × v² / L
- Potential energy: PE = m × g × L × (1 - cos(θ))
Here, m is mass, g is gravity, L is pendulum length, θ is angle from the lowest vertical position, α is angular acceleration, and v is speed at the selected angle.
How to Use This Calculator
- Enter the suspended mass and choose its unit.
- Enter the pendulum length from pivot to mass center.
- Enter the angle measured from the downward vertical line.
- Add angular acceleration when the load must speed up.
- Add speed when tension during motion is important.
- Add friction or resistance from guides, pulleys, bearings, or drag.
- Choose an output force unit.
- Press Calculate and review the result above the form.
Example Data Table
| Mass | Length | Angle | Acceleration | Approx Force | Use Case |
|---|---|---|---|---|---|
| 10 kg | 1.5 m | 15° | 0 rad/s² | 25.38 N | Slow holding check |
| 25 kg | 2 m | 30° | 0 rad/s² | 122.58 N | Manual pull estimate |
| 50 kg | 3 m | 45° | 0.2 rad/s² | 376.68 N | Actuator sizing |
| 100 lb | 6 ft | 20° | 0 rad/s² | 152.12 N | Shop rig planning |
Guide to Pendulum Force Planning
Why Angle Matters
A pendulum looks simple, but its load changes with angle. The required push is not the same at every point. Near the bottom, gravity pulls mostly through the string. At wider angles, more gravity acts along the path. This calculator converts that behavior into useful numbers.
Main Force Result
The main result is tangential force. It shows the force needed along the swing path. For a slow start or hold, the value depends on mass, gravity, and angle. When angular acceleration is added, the required force rises. This helps when a motor, hand winch, actuator, or test rig must move a suspended weight.
Torque and Length
Length also matters. It does not change the basic holding force, but it changes torque. A longer pendulum needs more turning moment at the pivot. The same force applied farther from the pivot creates a larger torque. That is why the tool reports both force and torque.
Tension and Motion
The calculator also estimates tension. Tension is the force carried by the rope, rod, chain, or cable. At rest, it depends on the radial component of weight. During motion, speed adds centripetal demand. That extra load can be important for safe hardware selection.
Energy Review
Energy values are useful too. The vertical rise shows how far the weight is lifted. Potential energy is mass times gravity times that rise. This is helpful when comparing motors, brakes, springs, or stored energy systems.
Practical Input Tips
Use realistic inputs. Enter the actual mass, pendulum length, angle, and expected speed. Add friction or allowance for bearings, pulleys, guides, and air drag. Use a safety factor when equipment or people could be harmed. The result is a planning estimate, not a replacement for engineering review.
Compare More Than One Case
Small angle changes can affect the answer. Test several angles before choosing hardware. Review the example table for typical cases. Then export the results for records, quotes, or design notes.
Unit Selection
Choose output units that match your shop standards. Newtons suit most design sheets. Pound-force may help with United States hardware catalogs. Kilogram-force is useful for quick load comparison. Keep angle measured from the lowest vertical position. Do not measure it from the horizontal. This convention keeps the formulas consistent across each result. Use one system when possible.
FAQs
What force does this calculator estimate?
It estimates tangential force along the pendulum path. It also reports holding force, safe force, torque, tension, height rise, arc distance, and potential energy.
Where should I measure the pendulum angle?
Measure the angle from the lowest vertical position. Zero degrees means the pendulum hangs straight down. Larger angles move the weight farther upward and sideways.
Does pendulum length change the required holding force?
Length does not change the basic tangential holding force for the same mass, gravity, and angle. It does change torque because torque equals force times length.
Why is speed included?
Speed affects tension through centripetal force. A moving pendulum can load the rope or rod more than a static pendulum at the same angle.
What is angular acceleration?
Angular acceleration shows how quickly the pendulum speed changes. Enter a positive value when the applied force must accelerate the weight along the swing path.
Should I add a safety factor?
Yes, use a safety factor when selecting hardware. It helps cover uncertainty, friction changes, shock loading, measurement error, and unexpected operating conditions.
Can I use pound-force results?
Yes. Select pound-force as the output unit. The calculator internally converts values, then displays the force result in your chosen unit.
Is this enough for final machine design?
No. Use it for planning and early sizing. Final designs should consider dynamic shock, material limits, fatigue, connection strength, controls, and professional engineering review.