Enter physics values
Required inputs are marked. Radius is optional and adds tangential acceleration.
Formula used
Angular acceleration uses the difference between final and initial angular velocity. Gravitational force uses Newton’s universal gravitation equation.
Here, α is angular acceleration, ω is angular velocity, Δt is elapsed time, G is 6.67430 × 10−11 N·m²/kg², m represents mass, and r is center-to-center separation.
How to use this calculator
- Enter initial and final angular velocities.
- Select the unit used for both angular velocity values.
- Enter a positive elapsed time and choose its unit.
- Add radius only when tangential acceleration is needed.
- Enter both masses, their units, and center-to-center separation.
- Select the separation unit, then choose Calculate results.
- Review SI outputs, export CSV, or print the page as a PDF.
Example data
| Input | Example value | Purpose |
|---|---|---|
| Initial angular velocity | 0 rpm | Starting rotation |
| Final angular velocity | 120 rpm | Rotation after acceleration |
| Elapsed time | 8 seconds | Acceleration interval |
| First mass | 5.972 × 1024 kg | Earth mass |
| Second mass | 7.348 × 1022 kg | Moon mass |
| Separation | 384,400 km | Earth–Moon center distance |
Understanding the calculations
Angular acceleration describes how rapidly rotational motion changes. It is measured in radians per second squared. A positive value indicates increasing angular speed. A negative value indicates slowing rotation. The magnitude ignores direction and reports the size of change. This calculator determines both the signed value and its magnitude.
The calculation starts with initial and final angular velocities. It then uses the elapsed time. Angular velocities can be entered in radians per second, degrees per second, or revolutions per minute. The tool converts every value to radians per second. Time can be given in seconds, minutes, or hours. The final calculation always uses SI units.
Gravitational force describes the attraction between two masses. Every mass attracts every other mass. The force grows as either mass grows. The force weakens quickly as separation increases. Distance is measured between the objects’ centers of mass. This detail matters for large bodies. Surface-to-surface spacing is not normally the required distance.
The calculator uses the universal gravitational constant. It converts mass inputs to kilograms. It converts distance to metres. Then it applies Newton’s inverse-square relationship. The output appears in newtons, kilonewtons, meganewtons, and pound-force. Scientific notation is included for very large or very small results.
Use consistent source measurements whenever possible. Small timing errors can change angular acceleration significantly. Distance errors can strongly affect gravitational force. This happens because distance is squared in the denominator. Double the separation and the force becomes one quarter. Halve the separation and the force becomes four times larger.
The optional radius field extends the rotational analysis. When a radius is supplied, the calculator finds tangential acceleration. Tangential acceleration shows the linear acceleration at that radius. It is useful for wheels, rotors, pulleys, and rotating machinery. A blank radius does not prevent the main calculations.
This tool is suitable for classroom checks and engineering estimates. It does not model air resistance, friction, deformation, relativity, or uneven mass distributions. Treat point-mass assumptions carefully. For planets and spheres, center-to-center distance is essential. For complex shapes, numerical modelling may be more appropriate.
Review the unit labels before calculating. Examine the signed angular acceleration and the magnitude separately. Use the export tools to preserve a calculation record. The included example demonstrates Earth and Moon gravitational attraction. Replace those values with your own measured data. Careful inputs produce useful, traceable physics results.
Before relying on a result, confirm what each number represents. Angular velocity is not ordinary linear speed. It measures turning rate around an axis. Mass must represent the total interacting amount, not a material density. Separation must be positive. The calculator rejects zero or negative time and distance values. Use more significant figures when values come from laboratory instruments. Round only when presenting the final answer. Keep the original units in your notes. They make later checking easier. They also help others reproduce calculations without confusion. This practice improves confidence in reported results.
Frequently asked questions
What does angular acceleration measure?
It measures how quickly angular velocity changes. Its SI unit is radians per second squared. A negative signed result means rotation slows in the chosen positive direction. The magnitude is always nonnegative.
Why must elapsed time be greater than zero?
The formula divides angular velocity change by elapsed time. Zero time would cause division by zero and has no usable physical interpretation here.
Which distance belongs in the gravitational formula?
Use the distance between the centers of mass. For planets, this is not the gap between surfaces. Using surface spacing can produce a seriously incorrect force.
Can I enter negative angular velocity?
Yes. Negative values can represent rotation opposite to your selected positive direction. The calculator preserves that sign while reporting a separate magnitude.
Why does force change so much with distance?
Gravitational force follows an inverse-square relationship. Doubling the separation reduces force to one quarter. Halving separation increases force by four times.
What is the optional radius used for?
Radius allows the calculator to find tangential acceleration. This is the linear acceleration at a point on a wheel, rotor, pulley, or similar rotating object.
Can masses be entered in pounds or grams?
Yes. Choose the matching mass unit. The calculator converts every mass to kilograms before applying the gravitational force equation.
Does this model include air resistance or friction?
No. The angular calculation uses only velocity change and time. The gravitational calculation uses an ideal point-mass model without extra forces.
Why are some answers shown in scientific notation?
Scientific notation keeps extremely large and extremely small values readable. It also helps preserve significant figures without a long string of zeros.
What does a negative angular acceleration mean?
It means angular velocity changed in the negative direction relative to the chosen convention. It may indicate slowing, reverse acceleration, or both.
How can I save my calculation?
Use Download CSV for a spreadsheet-ready record. After a result appears, choose Print / Save PDF to create a shareable document from your browser.