Question

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.

Answer 1

Answer:

(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

$\omega_{f}=\omega_{i}+\alpha t$

Put the value into the formula

$\omega_{f}=0.200+0.883\times0.204$

$\omega_{f}=0.380\ rev/s$

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

Using formula of angular displacement

$\theta=\omega_{i}t+\dfrac{1}{2}\alpha t^2$

Put the value into the formula

$\theta=0.200\times0.204+\dfrac{1}{2}\times0.883\times(0.204)^2$

$\theta=0.059\ rad$

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

Using formula of speed

$v=\dfrac{d}{2}\omega_{f}$

Put the value into the formula

$v=\dfrac{0.760}{2}\times0.380\times2\pi$

$v=0.907\ m/s$

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

Using formula of tangential acceleration

$a_{t}=\alpha r$

Put the value into the formula

$a_{t}=0.883\times0.38\times2\pi$

$a_{t}=2.10\ m/s^2$

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