Starting from rest, a blade of a rotor completes 20 revolutions in 4 seconds. As

Question

Starting from rest, a blade of a rotor completes 20 revolutions in 4 seconds. Assume that the angular acceleration is constant and find a) the angular acceleration, b) time to complete 40 revolutions, c) angular speed when it completes 40 revolutions and d) linear speed at a point 0.25 m from the axis of rotation when it completes 40 revolutions. For a) Does the statement "20 revolutions in 4 seconds" mean "20 revs/4 sec"? If that's the case, it's 5 revs/sec but I'm not sure if I need to convert to rad/s to answer the other question. If I need to find the angular acceleration, isn't it delta angular velocity divided by delta t (what if delta t is the given 4 seconds)? Please show work for question I will rate!!! Thanks!!

Explanation / Answer

a)2 = 360 degrees takes in one revolution

therefore

2*20 takes 4 seconds to do this so = 31.416 rad/s

a)=t

=7.854 rad/s^2

b)=40*2=80

=.5t^2

t=8 sec starting from rest

c)=8=62.832 rad/s

d)v=r=62.832*.25=15.71 m/s

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