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Physics Part-I

System of Particles and Rotational Motion

Two particles, each of mass m and speed v, travel in opposite

Physics Part-I

Class 11

NCERT

Chapter 1: Physical World

16 questions

Chapter 2: Units and Measurements

51 questions

Chapter 3: Motion in Straight Line

50 questions

Chapter 4: Motion in a Plane

43 questions

Chapter 5: Laws of motion

52 questions

Chapter 6: Work, Energy and Power

41 questions

Chapter 7: System of Particles and Rotational Motion

45 questions

Find the components along the x, y, z axes of the angular momentum

l

of a particle, whose position vector is

r

with components x, y, z and momentum is

p

with components

p_{x}, p_{y}

and

p_{z}

. Show that if the particle moves only in the x-y plane the angular momentum has only a z-component.

Two particles, each of mass

m

and speed

v

, travel in opposite directions along parallel lines separated by a distance

d

. Show that the vector angular momentum of the two particle system is the same whatever be the point about which the angular momentum is taken.

A non-uniform bar of weight

W

is suspended at rest by two strings of negligible weight as shown in fig. The angles made by the strings with the vertical are

36. 9^{o}

and

53. 1^{o}

respectively. The bar is

2 m

long. Calculate the distance d of the center of gravity of the bar from its left end.

View all question

Chapter 8: Gravitation

33 questions

Question

Medium

Solving time: 2 mins

Two particles, each of mass $m$ and speed $v$ , travel in opposite directions along parallel lines separated by a distance $d$ . Show that the vector angular momentum of the two particle system is the same whatever be the point about which the angular momentum is taken.

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Updated on: Oct 15, 2023

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Physics Part-I (NCERT)

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Two particles, each of mass

m

and speed

v

, travel in opposite directions along parallel lines separated by a distance

d

. Show that the vector angular momentum of the two particle system is the same whatever be the point about which the angular momentum is taken.

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

Let at a certain instant two particles be at points P and Q, as shown in the following figure.

Consider a point R, which is at a distance

y

from point Q, i.e.,

QR = y

∴

PR = d - y

Angular momentum of the system about point P:

L_{P} = m v \times 0 + m v \times d = m v d ...... (i)

Angular momentum of the system about point Q:

L_{Q} = m v \times d + m v \times 0 = m v d .... (ii)

Angular momentum of the system about point R:

L_{R} = m v \times (d - y) + m v \times y = m v d .... (iii)

Comparing equations (i), (ii), and (iii), we get:

L_{P} = L_{Q} = L_{R} ...... (i v)

We infer from equation

(i v)

that the angular momentum of a system does not depend on the point about which it is taken.

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Practice more questions from Physics Part-I (NCERT)

Find the components along the x, y, z axes of the angular momentum

l

of a particle, whose position vector is

r

with components x, y, z and momentum is

p

with components

p_{x}, p_{y}

and

p_{z}

. Show that if the particle moves only in the x-y plane the angular momentum has only a z-component.

Two particles, each of mass

m

and speed

v

, travel in opposite directions along parallel lines separated by a distance

d

. Show that the vector angular momentum of the two particle system is the same whatever be the point about which the angular momentum is taken.

A non-uniform bar of weight

W

is suspended at rest by two strings of negligible weight as shown in fig. The angles made by the strings with the vertical are

36. 9^{o}

and

53. 1^{o}

respectively. The bar is

2 m

long. Calculate the distance d of the center of gravity of the bar from its left end.

View all

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Question Text	Two particles, each of mass $m$ and speed $v$ , travel in opposite directions along parallel lines separated by a distance $d$ . Show that the vector angular momentum of the two particle system is the same whatever be the point about which the angular momentum is taken.
Updated On	Oct 15, 2023
Topic	System of Particles and Rotational Motion
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 3
Upvotes	362
Avg. Video Duration	20 min

Two particles, each of mass $m$ and speed $v$ , travel in opposite directions along parallel lines separated by a distance $d$ . Show that the vector angular momentum of the two particle system is the same whatever be the point about which the angular momentum is taken.

Text solutionVerified

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Two particles, each of mass m and speed v, travel in opposite directions along parallel lines separated by a distance d. Show that the vector angular momentum of the two particle system is the same whatever be the point about which the angular momentum is taken.

Text solutionVerified

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Two particles, each of mass $m$ and speed $v$ , travel in opposite directions along parallel lines separated by a distance $d$ . Show that the vector angular momentum of the two particle system is the same whatever be the point about which the angular momentum is taken.