Question

An electric ceiling fan is rotating about a fixed axis with an initial angular velocity magnitude of 0.280 rev/s . The magnitude of the angular acceleration is 0.893 rev/ s 2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.710 m .

Part A

Compute the fan's angular velocity magnitude after time 0.191 s has passed. Express your answer numerically in revolutions per second.

Part B

Through how many revolutions has the blade turned in the time interval 0.191 s from Part A? Express the number of revolutions numerically.

Part C

What is the tangential speed v tan (t) of a point on the tip of the blade at time t = 0.191 s ? Express your answer numerically in meters per second.

Part D

What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t = 0.191 s ? Express the acceleration numerically in meters per second squared.

Answer 1

Given that, = angular acceleration = 0.893 rev/s² = 5.611 rad/s² (1 rev = 2 rad)

= initial angular velocity = 0.280 rev/s = 1.759 rad/s

= is the final angular velocity

R = the radius of the circle of revolution = 0.710/2 = 0.355 m

Part A: The equation of rotational motion, , the final angular velocity will be

Part B: The number of revolution will be 0.451

Part C: Tangential speed is the linear speed after time t = 0.191 s. which is equal to

Part D: The magnitude a of the resultant acceleration of a point on the tip of the blade at time t = 0.191 s will be