A fan blade, whose diameter is 2 m, starts turning from rest with constant angul

Question

A fan blade, whose diameter is 2 m, starts turning from rest with constant angular

   acceleration of 5 rev/s2.

a) What is the tangential velocity of a point on the tip of the blade after 2 seconds ?

   Show direction of the tangential velocity.

b) Find the centripetal acceleration of a point on the tip of the blade after 2 seconds.

   Show direction of centripetal acceleration.

c) Through what angle will the a point on the tip of the blade be displaced from its

   original position after 2 seconds?

Explanation / Answer

a)

Tangential acceleration=dv/dt

v=5*2=10 m/s

b)

a=V^2/R=100/1=100 m^2/sec

c)

Say at initial condition top point is A and this point is moved to point B after t=2 sec

Say vertical distance between A and B is h

apply energy conservation

m*g*h=0.5*m*vf^2-0.5*m*vi^2

h=0.5*vf^2/g=0.5*100/10=5m

Note: i don't know why here h is coming greater than R

so angle between point A and B =acos(R-h/R)

hence distance=R*Theta

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