Chapter 4: Q.69 (page 109)

A high-speed drill rotating ccw at $2400 rpm$ comes to a halt in $2.5 s$ .
a. What is the magnitude of the drill’s angular acceleration?
b. How many revolutions does it make as it stops?

Short Answer

Expert verified

a. The magnitude of the drill’s angular acceleration $- 100 rad / s^{2}$ .

b. $50 rev$ it make as it stops.

Step by step solution

Given information

$ω_{i} = 2400 rpm$

$ω_{f} = 0$

$t = 2.5 s$

Part a) Step 1: Calculation

To convert angular velocity from revolution per minutes to the revolution per second:

$ω_{i} = 2400 \frac{rev}{\min} \times \frac{1 \min}{60 s} \times \frac{2 π rad}{1 rev} ω_{i} = 251 rad / s$

To calculate angular acceleration:

α = \frac{ω_{f} - ω_{i}}{t} α = \frac{0 rad / s - 251 rad / s}{2.5 s} α = - 100 rad / s^{2}

Part b) Step 1: Calculation

To calculate number of revolution

2 θ = (ω_{f} + ω_{i}) t θ = \frac{(ω_{f} + ω_{i}) t}{2} θ = \frac{(0 rad / s + 251 rad / s) (2.5 s)}{2} θ = \frac{(251 rad / s) (2.5 s)}{2} θ = 313.75 rad

To convert radian in revolutions

$θ = 2 πN N = \frac{θ}{2 π} N = \frac{313.75 rad}{(2) (3.14 rad)} N = 49.96 rev N = 50 rev$

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A high-speed drill rotating ccw at $2400 rpm$ comes to a halt in $2.5 s$ .
a. What is the magnitude of the drill’s angular acceleration?
b. How many revolutions does it make as it stops?

Short Answer

Step by step solution

Given information

Part a) Step 1: Calculation

Part b) Step 1: Calculation

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A high-speed drill rotating ccw at 2400rpmcomes to a halt in 2.5s. a. What is the magnitude of the drill’s angular acceleration?b. How many revolutions does it make as it stops?

Short Answer

Step by step solution

Given information

Part a) Step 1: Calculation

Part b) Step 1: Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Magnetism

Fluids

Quantum Physics

Wave Optics

Dynamics

Scientific Method Physics

Study anywhere. Anytime. Across all devices.

A high-speed drill rotating ccw at $2400 rpm$ comes to a halt in $2.5 s$ .
a. What is the magnitude of the drill’s angular acceleration?
b. How many revolutions does it make as it stops?