A circular saw blade is at rest when the saw is suddenly turned on. As the blade

Question

A circular saw blade is at rest when the saw is suddenly turned on. As the blade spins it acquires a rotation rate corresponding to a frequency of 480 rotations per minute. It takes 2 seconds for the blade to acquire this angular speed. (a) Find the angular acceleration of the saw blade during the 2 sec time interval. (b) How many rotations (2 pi rads in each rotation) does the blade complete as it starts up? (c) Suppose the blade runs at this operating rate of 480 rpm's as mentioned above and is then turned off. If it completes 28 complete rotations (2 pi rads in each rotation) as it slows down to rest, find the angular acceleration of the blade as it slows down.

Explanation / Answer

initial angular speed=wi=0

final angular speed=wf=480 rotation per min=50.26 rad/sec

angular accleration=a=(wf-wi)/t=25.13 rad/s^2

(b) Angle covered=0.5*a*t^2=50.26 rad=8 revolution

(c)now

initial speed=16*pi=50.26 rad/sec

final speed=0 rad/s

A=angle covered=28*2*pi

angular accleration=(wi^2)/(2*A)=-7.18 rad/s^2

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