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Work by a constant force
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Calculators / Science / Angular displacement
Angular displacement calculator
Calculate angular displacement under constant angular acceleration.
On this page
Angular displacement10.5rad
Final angular velocity5rad/s
Calculator controls
How to calculate
Calculate angular displacement under constant angular acceleration.
Angular displacement = w*t+a*t^2/2 rad; Final angular velocity = w+a*t rad/s
Worked example
Initial angular velocity (rad/s): 2; Constant angular acceleration (rad/s²): 1; Elapsed time (s): 3.
Angular displacement: 10.5 rad; Final angular velocity: 5 rad/s.
Assumptions and limits
Angular acceleration must remain constant throughout the interval. Signed angular velocities refer to one rotation axis; reversing direction does not reset the accumulated angle.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Calculate angular displacement under constant angular acceleration.
When this tool is useful
Angular displacement = w*t+a*t^2/2 rad; Final angular velocity = w+a*t rad/s
Understanding your inputs
| Input | What to enter |
|---|---|
| Initial angular velocity (rad/s) | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Constant angular acceleration (rad/s²) | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Elapsed time (s) | Enter a number of at least 0 and no more than 1000000000000. |
Frequently asked questions
What assumptions does this calculation use?
Angular acceleration must remain constant throughout the interval. Signed angular velocities refer to one rotation axis; reversing direction does not reset the accumulated angle.
How is the result calculated?
Angular displacement = w*t+a*t^2/2 rad; Final angular velocity = w+a*t rad/s