Chapter 4: Q.75 (page 109)

A painted tooth on a spinning gear has angular acceleration $α = (20 - t) rad / s^{2}$ , where t is in s. Its initial angular velocity, at $t = 0 s$ , is $300 rpm$ . What is the tooth’s angular velocity in rpm at $t = 20 s$ ?

Short Answer

Expert verified

The tooth’s angular velocity is $2210 rpm$ .

Step by step solution

Given information

$angular acceleration = α = (20 - t) rad / s^{2} angular velocity = ω_{1} = 300 rpm$

Calculation

The angular acceleration is:

$α = \frac{dω}{dt} dω = α . dt dω = [(20 - t) rad / s^{2}] dt \int_{ω_{1}}^{ω_{2}} dω = \int_{0}^{20} [(20 - t) rad / s^{2}] dt ω_{2} - ω_{1} = [(20) (20) - (\frac{1}{2}) {(20)}^{2}] rad / s ω_{2} - ω_{1} = 200 rad / s$

Now converting angular velocity from radian per second to revolution per minute:

$ω_{2} - ω_{1} = 200 \frac{rad}{s} \times \frac{60 s}{1 \min} \times \frac{1 rev}{2 π rad} ω_{2} - ω_{1} = 1910 rpm$

The tooth’s angular velocity

$ω_{2} = 1910 rpm + ω_{1} ω_{2} = 1910 rpm + 300 rpm ω_{2} = 2210 rpm$

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A painted tooth on a spinning gear has angular acceleration $α = (20 - t) rad / s^{2}$ , where t is in s. Its initial angular velocity, at $t = 0 s$ , is $300 rpm$ . What is the tooth’s angular velocity in rpm at $t = 20 s$ ?

Short Answer

Step by step solution

Given information

Calculation

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A painted tooth on a spinning gear has angular acceleration α=(20-t)rad/s2 , where t is in s. Its initial angular velocity, at t=0s, is 300rpm. What is the tooth’s angular velocity in rpm at t=20s?

Short Answer

Step by step solution

Given information

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Famous Physicists

Classical Mechanics

Conservation of Energy and Momentum

Measurements

Scientific Method Physics

Wave Optics

Study anywhere. Anytime. Across all devices.

A painted tooth on a spinning gear has angular acceleration $α = (20 - t) rad / s^{2}$ , where t is in s. Its initial angular velocity, at $t = 0 s$ , is $300 rpm$ . What is the tooth’s angular velocity in rpm at $t = 20 s$ ?