Angular Acceleration

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In circular motion, the acceleration in the angular path is called the angular acceleration. We can define it as the change in angular velocity with respect to time is known as Angular acceleration. It is represented by  “α”.  Angular acceleration is a vector quantity that means it has both magnitude and direction.

The S.I unit of angular acceleration is given rad/s^2.

α = dω/dt

 and   α = d^2θ/dt^2

Where, ω = angular acceleration

              t = time taken

             θ = rotated angle

We are using frequency also to relate the revolution to the angular velocity.

 Frequency = revolution/time

And   ω = 2? f

Here, f is frequency.

Also linear velocity, v = rω  

  And linear acceleration, a = v^2/r

 
Example: A flywheel, diameter 2.8m, rotating at 1800 rev/min slows down at a constant rate to 1200 rev/min in 40 s. Find the angular acceleration.

Solution: Given that,

          Radius = 2.8/2 = 1.4 m

          Initial Frequency, f1 = 1800 rev/min = 1800/60 = 30 rev/sec

          So, ω = 2?f = 2x3.14x30 = 188.4 rad/s

And   final frequency, f2 = 1200 rev/min = 1200/60 = 20 rev/sec

          So, ω = 2?f = 2x3.14x20 = 125.7 rad/s

Hence,       angular acceleration, α = (125.7 – 188.4)/40 = 1.56 rad/s^2

 
Example: The spin dryer in a washing machine is a cylinder with diameter 600mm. It spins at 1200 rev/min.
Find linear 
velocity, acceleration and angular acceleration.

Solution: Given that,

          Frequency, f = 1200/60 = 20 rev/sec

          So,    ω = 2?f = 2x3.14x20 = 125.7 rad/sec

Linear velocity, v = rω = (600/2) x 0.001 x 125.7 = 37.71 m/s

Acceleration, a = v^2/r = 4740 m/s^2

 

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