Difference between revisions of "Angular impulse"
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| − | The '''angular impulse''' in [[physics]] is the product of the average of a briefly applied force ''F'' times the radius of a rigid body ''R'' times the brief time period | + | The '''angular impulse''' in [[physics]] is the product of the average of a briefly applied force ''F'' times the radius of a rigid body ''R'' times the brief time period ''δt'': |
| − | :<math>\mathbf{F}\times{R}\times\delta{t}= I \times( | + | :<math>\mathbf{F}\times{R}\times\delta{t}= I \times(\omega_f - \omega_i)</math> |
where the final angular velocity is just after the impulse, and the initial angular velocity is just before the impulse. | where the final angular velocity is just after the impulse, and the initial angular velocity is just before the impulse. | ||
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== Example == | == Example == | ||
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Suppose a rotating cylinder of radius R<sub>2</sub> is joined with a stationary cylinder of radius R<sub>1</sub>. Both feel an impulsive force until the continue rotating without slippage at different angular velocities. The above formula permits calculation of the respective angular velocities as follows: | Suppose a rotating cylinder of radius R<sub>2</sub> is joined with a stationary cylinder of radius R<sub>1</sub>. Both feel an impulsive force until the continue rotating without slippage at different angular velocities. The above formula permits calculation of the respective angular velocities as follows: | ||
| − | :<math>\mathbf{ | + | :<math>\mathbf{F_1}\times\delta{t_1}= -\mathbf{F_2}\times\delta{t_2}</math> |
Thus: | Thus: | ||
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:<math>\omega_{f1} = \frac{\omega_{f2}\times{R_2}}{R_1}</math> | :<math>\omega_{f1} = \frac{\omega_{f2}\times{R_2}}{R_1}</math> | ||
| − | and thus <math>\omega_{f2} can be solved in terms of the initial velocity of the rotating cylinder <math>\omega_{i1}. | + | and thus <math>\omega_{f2}</math> can be solved in terms of the initial angular velocity of the rotating cylinder <math>\omega_{i1}</math>. |
| + | |||
| + | ==See also== | ||
| + | *[[Rotational mechanics]] | ||
| + | *[[Impulse]] | ||
| − | [[Category: | + | [[Category:Physics]] |
| + | [[Category:Mechanics]] | ||
Latest revision as of 17:47, September 5, 2017
The angular impulse in physics is the product of the average of a briefly applied force F times the radius of a rigid body R times the brief time period δt:
where the final angular velocity is just after the impulse, and the initial angular velocity is just before the impulse.
Example
Suppose a rotating cylinder of radius R2 is joined with a stationary cylinder of radius R1. Both feel an impulsive force until the continue rotating without slippage at different angular velocities. The above formula permits calculation of the respective angular velocities as follows:
Thus:
But:
and:
and thus 
can be solved in terms of the initial angular velocity of the rotating cylinder 
.
