angular impulse formulas and interpretation
Angular impulse is the change in angular momentum produced by torque acting over time.
The calculator also relates the same momentum change to moment of inertia and angular velocity change.
How to use the angular impulse calculator
- Choose a model: Select the physical relationship that matches the known values.
- Choose the unknown: Select the quantity you need to calculate.
- Enter values and units: Provide every requested measurement using consistent units.
- Calculate: Check the formula, converted result, sign, and units.
Formula and variables
Angular impulse equals average net torque multiplied by its time interval and equals the change in angular momentum.
Jθ = τΔt = ΔL- Jθ — Angular impulse
- Change in angular momentum (N·m·s)
- τ — Torque
- Average net torque (N·m)
- Δt — Time interval
- Duration of applied torque (s)
Applied torque example
A 12 N·m torque acts for 3 seconds.
- Torque
- 12 N·m
- Time
- 3 s
- Jθ = 12 × 3
- Jθ = 36 N·m·s
Result: Angular impulse is 36 N·m·s.
Angular momentum changes by 36 kg·m²/s.
Understanding your results
Interpreting the result
For constant average torque, angular impulse grows in direct proportion to torque and duration.
A sign indicates direction only when a consistent rotational sign convention is used.
Assumptions
- Rotation is evaluated about a specified axis.
- Inputs are converted through coherent SI units.
- The selected formula adequately represents the physical system.
Limitations
- The calculator does not simulate time-varying inputs.
- Vector directions and multiple axes must be resolved separately.
- Losses such as friction are not added unless represented in the entered net value.
Common mistakes
- Mixing RPM with radians per second.
- Using diameter instead of radius.
- Entering a zero divisor.
- Ignoring the direction represented by a negative value.
Practical use cases
Physics and education
Check rotational kinematics and dynamics exercises.
Machines and mechanisms
Estimate quantities for wheels, shafts, rotors, and rotating equipment.
Frequently asked questions
Why are radians used in rotational formulas?
Radians make angular and linear relationships dimensionally coherent without an extra conversion factor.
Can the result be negative?
Yes. A negative value means the quantity points opposite the direction chosen as positive.
Sources and review
- SI Brochure, 9th edition — BIPM. Accessed 2026-07-11.
- Special Publication 811 — NIST. Accessed 2026-07-11.
Reviewed 2026-07-11.