Long Physics problem?

Question

An electric ceiling fan is rotating about a fixed axis with an initial angular velocity of 0.220 rev/s. The angular acceleration is 0.883 rev/s^2 . Its blades form a circle of diameter 0.800 m.

Compute the angular velocity of the fan after time 0.207 s has passed.

How many revolutions has the blade turned in the time interval 0.207 s.

What is the tangential speed of a point on the tip of the blade at time = 0.207 s?

What is the magnitude of the resultant acceleration of a point on the tip of the blade at time = 0.207 s ?

Answer 1

w2 = w1 +w’*t, where w1=0.22 rev/s, w’=0.883 rev/s^2, t=0.207;

w2=0.402781 rev/s;

n =w1*t+0.5*w’*t^2 = 0.064458 revolutions;  

v=w2*r =(0.402781*2pi) *(0.800/2) =1.0123 m/s;

a=√(a1^2 +a2^2), where a1=w’*r is tangential acceleration, a2=v^2/r is centripetal acceleration;

a=√[(0.883*2pi)^2 *(0.8/2)^2 +(1.0123)^4 /(0.8/2)^2] =3.39 m/s^2;