Chapter 12: Q. 3 (page 330)

A ceiling fan with 80 cm-diameter blades is turning at 60 rpm. Suppose the fan coasts to a stop 25s after being turned off.

Short Answer

Expert verified

The speed of the tip of the blade is 1.15 m/s

The number of revolutions is 12.5 rev

Step by step solution

Step 1. Given information

The diameter of the fan is 80 cm, its angular velocity is 60 rpm , and it needs to 25 seconds to stop.

The radius of the blade is $r = 40 cm$ ,

$d = (40 cm) (\frac{0.01 m}{1 cm}) = 0.4 m$

Initial angular speed of the fan is

$ω_{i} = (60 \frac{rev}{min}) (\frac{2 π rad}{1 rev}) (\frac{1 min}{60 s}) = 6.28 rad / s$

The angular acceleration of the fan is,

$α = \frac{ω_{f} - ω_{i}}{Δ t} = \frac{0 - 6.28 rad / s}{25 s} = - 0.251 rad / s^{2}$

Part (a)

The angular speed of the tip of the blade is

$ω_{f} = ω_{i} + α t = 6.28 rad / s + (- 0.251 rad / s^{2}) (10 s) = 3.77 rad / s$

The speed of the tip of the blade is,

$v = r ω_{f} = (0.4 m) (3.77 rad / s) = 1.51 m / s$

Therefore, speed of the tip of the blade is $1.51 m / s$ .

Part (b)

The number of revolutions, in $Δ t = 25 s$

$\begin{array}{l} Δ θ = ω_{i} Δ t + \frac{1}{2} α {(Δ t)}^{2} \\ = (6.28 rad / s) (25 s) + \frac{1}{2} (- 0.251 rad / s^{2}) {(25 s)}^{2} \\ = (78.6 rad) (\frac{1 rev}{2 π rad}) \\ = 12.5 rev \end{array}$

Therefore, the number of revolutions is $12.5 rev$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

A ceiling fan with 80 cm-diameter blades is turning at 60 rpm. Suppose the fan coasts to a stop 25s after being turned off.

Short Answer

Step by step solution

Step 1. Given information

Part (a)

Part (b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Linear Momentum

Electromagnetism

Fluids

Electric Charge Field and Potential

Torque and Rotational Motion

Geometrical and Physical Optics

Study anywhere. Anytime. Across all devices.