How Do You Calculate Angular Acceleration with Only Velocity and Radius?

[Nanabit]

How do you find angular acceleration when all you have is angular and linear velocity and a radius of a circle? I tried to use the kinematics but all of them require time or theta.

 

[StephenPrivitera]

If you know the angular velocity, you need only to take the derivative of this to get the angular acceleration.
If the angular velocity is constant, then the angular acceleration is 0.

 

[M98Ranger]

Angular acceleration is the rate of change of angular velocity over time. It is represented by the symbol alpha (α) and is measured in radians per second squared (rad/s^2).

To find angular acceleration when given angular and linear velocity and a radius of a circle, you can use the formula α = v/r, where v is the linear velocity and r is the radius. This formula can be derived from the kinematic equations, specifically the equation that relates linear and angular velocity, v = ωr.

If you do not have a specific time or angle (theta) given, you can still use this formula to find the average angular acceleration over a certain period of time or angle. For example, if you have the initial and final angular and linear velocities, you can use the formula α = (ωf - ωi)/t or α = (θf - θi)/t, where t is the time or theta interval.

However, if you are looking for the instantaneous angular acceleration at a specific moment, you will need to have either the time or angle at that moment to use the kinematic equations. If you have neither, you may need to use other methods, such as calculus, to find the angular acceleration.

In summary, angular acceleration can be found using the formula α = v/r when given angular and linear velocity and a radius. If time or angle is not given, you can still find the average angular acceleration over a period of time or angle. However, to find the instantaneous angular acceleration, you will need to have either the time or angle at that specific moment.