An electric ceiling fan is rotating about a fixed axis with an initial angular velocity magnitude of 0.200 rev/s . The magnitude of the angular acceleration is 0.883 rev/s2 . Both the the angular velocity and angular accleration are directed counterclockwise. The electric ceiling fan blades form a circle of diameter 0.760 m .A. Compute the fan's angular velocity magnitude after time 0.204 s has passed. Express your answer numerically in revolutions per second. B. Through how many revolutions has the blade turned in the time interval 0.204 s from Part A?Express the number of revolutions numerically. C. What is the tangential speed vt of a point on the tip of the blade at time t = 0.204 s?Express your answer numerically in meters per second. D. Calculate the magnitude atat of the tangential acceleration of a point on the tip of the blade at time t = 0.204 s. Express the acceleration numerically in meters per second squared.

(A). the angular velocity of fan is 0.380 rev/s.

(B). The number of revolution is 0.059 rad.

(C). The tangential speed of the blade is 0.907 m/s.

(D). The tangential acceleration of the blade is 2.10 m/s²

Explanation:

Given that,

Initial angular velocity = 0.200 rev/s

Angular acceleration = 0.883 rev/s²

Diameter = 0.760 m

Time = 0.204 s

(A). We need to calculate the angular velocity of fan

Using equation of angular motion

Put the value into the formula

(B). We need to calculate the number of revolution

Using formula of angular displacement

Put the value into the formula

(C). We need to calculate the tangential speed of the blade

Using formula of speed

Put the value into the formula

(D). We need to calculate the tangential acceleration of the blade

Using formula of tangential acceleration

Put the value into the formula

Hence, (A). the angular velocity of fan is 0.380 rev/s.

(B). The number of revolution is 0.059 rad.

(C). The tangential speed of the blade is 0.907 m/s.

(D). The tangential acceleration of the blade is 2.10 m/s²

acceleration = (change in speed) / (time for the change)

change in speed = (20-120)= -100 m/s.

1.5 min = 90 sec

acceleration = -100/90 = -1.11 m/s^2.

we don't care about the 150kg or the 2,500 meters. they don't make any difference.

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