Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

Two particles, each of mass $2.90 \times 10^{- 4} kg$ and speed 5.46 m/s, travel in opposite directions along parallel lines separated by 4.20 cm. (a) What is the magnitude L of the angular momentum of the two-particle system around a point midway between the two lines? (b) Is the value different for a different location of the point? If the direction of either particle is reversed, what are the answers for (c) part (a) and (d) part (b)?

The magnitude L of the angular momentum of the two-particle system around a point midway between the two lines is $L = 6.65 \times 10^{- 5} kg . m^{2} / s$ .
The value is not different for a different location of the point.
If the direction of either particle is reversed, the answer for part (a) is zero.
If the direction of either particle is reversed, then the value is different for different locations of a point.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given Data

$m = 2.90 \times 10^{- 4} kg V = 5.46 m / s d = 4.20 cm$

Step 2: Determining the concept

Using the formula for angular momentum, determine the magnitude and direction of the angular momentum.

Formula is as follow:

$L = m \times v \times d$

Where, m is mass, d is distance, v is velocity and L is angular momentum.

Step 3: (a) Determining the magnitude L of the angular momentum of the two-particle system around a point midway between the two lines

To calculate angular momentum, use the following formula:

$L = m \times v \times r + m \times v \times r L = 2 \times m \times v \times r L = m \times v \times d L = 2.90 \times 10^{- 4} \times 5.46 \times 0.042 L = 6.65 \times 10^{- 5} kg . m^{2} / s$

Hence, the magnitude L of the angular momentum of the two-particle system around a point midway between the two lines is $L = 6.65 \times 10^{- 5} kg . m^{2} / s$ .

Step 4: (b) Determining if value different for a different location of the point

If location of point is changed then the angular momentum doesn’t change.

Hence, the value is not different for a different location of the point.

Step 5: (c) Determining if the direction of either particle is reversed, what is the answer for part (a)

If the direction of any one of the particles changes, the angular momentum becomes zero; because angular momentum is vector quantity. As the direction changes, the angular momentum of both particles are in opposite directions, so they cancel out each other.

Hence, if the direction of either particle is reversed, the answer for part (a) is zero.

Step 6: (d) Determining if the direction of either particle is reversed, what is the answer part (b)

Since, the result depends on the choice of axis, so yes, the value would be different for different locations of points.

Hence, if the direction of either particle is reversed, then the value is different for different locations of a point.

Therefore, using the formula for angular momentum, angular momentum can be found with given conditions.

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Fundamentals Of Physics

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Short Answer

Step by Step Solution

Step 1: Given Data

Step 2: Determining the concept

Step 3: (a) Determining the magnitude L of the angular momentum of the two-particle system around a point midway between the two lines

Step 4: (b) Determining if value different for a different location of the point

Step 5: (c) Determining if the direction of either particle is reversed, what is the answer for part (a)

Step 6: (d) Determining if the direction of either particle is reversed, what is the answer part (b)

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Fundamentals Of Physics

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Short Answer

Step by Step Solution

Step 1: Given Data

Step 2: Determining the concept

Step 3: (a) Determining the magnitude L of the angular momentum of the two-particle system around a point midway between the two lines

Step 4: (b) Determining if value different for a different location of the point

Step 5: (c) Determining if the direction of either particle is reversed, what is the answer for part (a)

Step 6: (d) Determining if the direction of either particle is reversed, what is the answer part (b)

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