Angular Acceleration Equation

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As we know that the acceleration is the rate of change of velocity but in angular acceleration it is the rate of change of angular velocity of an object.

Angular acceleration is represented by alpha “α”. Its unit is rad/s^2.

α = dω/dt

α = (ωf – ωi)/(tf – ti)

Where,

ωf and ωi = final and initial angular velocity

tf and ti = final and initial time

  ω = v/r

 also  ω = θ/t

where, v = linear velocity

            r = radius of circular path

            θ = rotated angle
Thus,                  
           α = d^2θ/dt^2

 
Example: The angular velocity is changing at the rate of 28 rad/s for 4 s. Calculate the angular acceleration?


Solution: Given that

  Angular velocity = 28 rad/sec

  Time = 4 Sec

So that,  α = dω/dt

  = 28/4 = 7 rad/s^2

Example:  A wheel of a bicycle has an angular acceleration of 25 rad/s2 in 5 second. Find the angular velocity?

Solution: Given that,

  Angular acceleration = 25 rad/s^2

  Time = 5 sec

Now, we have

   α = dω/dt

dω = αdt = 25 x 5 = 125 rad/sec
 
 

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