Question

An electric ceiling fan is rotating about a fixed axis with an initial angular velocity magnitude of 0.240 rev/s. The magnitude of the angular acceleration is 0.917 rev/s^2. Both the the angular velocity and angular acceleration are directed counterclockwise. The electric ceiling fan blades form a circle of diameter 0.720 m. a) Compute the fan's angular velocity magnitude after time 0.203 s has passed.Compute the fan's angular velocity magnitude after time 0.203 s has passed. Express your answer numerically in revolutions per second. b) What is the tangential speed vt of a point on the tip of the blade at time t = 0.203 s? Express your answer numerically in meters per second. c) Calculate the magnitude at of the tangential acceleration of a point on the tip of the blade at time t= 0.203 s. Express the acceleration numerically in meters per second squared.

Answer 1

Explanation:

Given that,

Angular velocity = 0.240 rev/s

Angular acceleration = 0.917 rev/s²

Diameter = 0.720 m

(a). We need to calculate the angular velocity after time 0.203 s

Using equation of angular motion

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

Put the value in the equation

$\omega_{f}=0.240+0.917\times0.203$

$\omega_{f}=0.426\ rev/s$

The angular velocity is 0.426 rev/s.

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

Using formula of  tangential speed

$v= r\omega$

Put the value into the formula

$v = \dfrac{0.720 }{2}\times0.426\times2\pi$

$v=0.963\ m/s$

The tangential speed of the blade is 0.963 m/s.

(c). We need to calculate the magnitude at of the tangential acceleration

Using formula of tangential acceleration

$a_{t}=r\alpha$

Put the value into the formula

$a_{t}=0.36\times0.917\times2\pi$

$a_{c}=2.074\ m/s^2$

The tangential acceleration is 2.074 m/s².

Hence, This is required solution.