Chapter 12: Q. 1 (page 330)

A high-speed drill reaches $2000 rpm$ in $0.50 s$ .
a. What is the drill's angular acceleration?
b. Through how many revolutions does it turn during this first $0.50 s$ ?

Short Answer

Expert verified

(a) The angular acceleration is $419 rad / s^{2}$

(b) The number of revolution is $8.30 rev$ .

Step by step solution

Step 1. Given information

(a) The change in angular velocity, $Δ ω = 2000 \frac{rev}{min}$

(b) The change in time interval, $Δ t = 0.50 s$

The expression for angular displacement in a given time interval is,

$θ (t) = ω_{i} Δ t + \frac{1}{2} α {(Δ t)}^{2}$

Here, $ω_{i}$ is the initial velocity, $Δ t$ is the time interval and is angular acceleration.

Part (a)

The angular acceleration.

$\begin{array}{l} α = \frac{Δ ω}{Δ t} \\ α = \frac{2000 rpm (\frac{2 π}{1 rotation}) (\frac{1 min}{60 s})}{0.5 s} = 418.6 rad / s^{2} \\ α \approx 419 rad / s^{2} \end{array}$

Part (b)

The number of revolutions turned during the first is given by,

$\begin{array}{l} θ (t) = ω_{i} Δ t + \frac{1}{2} α {(Δ t)}^{2} \\ θ (t) = (0) Δ t + \frac{1}{2} (419 rad / s^{2}) {(0.5 s)}^{2} \\ θ (t) = 52.4 rad (\frac{1 rev}{2 π rad}) = 8.30 rev \end{array}$

Therefore, the number of revolution $0.5 s$ in is $8.30 rev$ .

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A high-speed drill reaches $2000 rpm$ in $0.50 s$ .
a. What is the drill's angular acceleration?
b. Through how many revolutions does it turn during this first $0.50 s$ ?

Short Answer

Step by step solution

Step 1. Given information

Part (a)

Part (b)

One App. One Place for Learning.

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A high-speed drill reaches 2000rpmin0.50s .a. What is the drill's angular acceleration?b. Through how many revolutions does it turn during this first 0.50s?

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

Fluids

Dynamics

Torque and Rotational Motion

Work Energy and Power

Atoms and Radioactivity

Thermodynamics

Study anywhere. Anytime. Across all devices.

A high-speed drill reaches $2000 rpm$ in $0.50 s$ .
a. What is the drill's angular acceleration?
b. Through how many revolutions does it turn during this first $0.50 s$ ?