An electric ceiling fan is rotating about a fixed axis with an initial angular v

Question

An electric ceiling fan is rotating about a fixed axis with an initial angular velocity magnitude of 0.230rev/s . The magnitude of the angular acceleration is 0.887rev/s2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.720m.

A) The fan's angular velocity magnitude after time 0.203s has passed is 0.410 rev/s.

B) The blade has turned 0.065 rev in the time interval 0.203s from part A.

C) What is the tangential speed vtan(t) of a point on the tip of the blade at time t= 0.203s ?

D) What is the magnitude (alpha) of the resultant acceleration of a point on the tip of the blade at time t= 0.203s?

I just need help on parts C and D!

Explanation / Answer

C)

Here , w = 0.410 rev/s

Now , Vtan   = r*w

Vtan = 0.410 * 6.282 * 0.36

Vtan = 0.93 m/s

the tangential speed is 0.93 m/s

D)

Here ,

at = r*a

at = 0.887 * 6.282 *0.36

at = 2 m/s^2

ac = v^2/r

ac = 0.93^2/.36

ac = 2.4 m/s^2

resultant acceleration = sqrt(ac^2 + at^2)

resultant acceleration = sqrt(2.4^2 + 2^2)

resultant acceleration =3.13 m/s^2

the magnitude of resultant acceleration is 3.13 m/s^2

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