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A unit mass at position vector r = 3 ICAP + 4 j cap is moving with velocity v is equals to 5 ICAP minus 6 j cap what is the angular momentum of the body about the origin?
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A unit mass at position vector r = 3 ICAP + 4 j cap is moving with vel...
To determine the angular momentum of a unit mass moving in a two-dimensional plane about the origin, we can follow a systematic approach.
Position Vector
- The position vector r of the mass is given as:
r = 3 i + 4 j
Velocity Vector
- The velocity vector v of the mass is:
v = 5 i - 6 j
Angular Momentum Formula
- The angular momentum L about the origin is calculated using the formula:
L = r × p
where p is the linear momentum, given by p = mv.
Since the mass m = 1, p = v.
Calculating Linear Momentum
- Therefore, the linear momentum p is:
p = 5 i - 6 j
Cross Product Calculation
- Now, we calculate the cross product of r and p:
L = r × p
= (3 i + 4 j) × (5 i - 6 j)
- Using the determinant method, we set up the matrix:
| i j k |
| 3 4 0 |
| 5 -6 0 |
- The determinant yields:
L = (0 - 0) i - (0 - 15) j + (-18 - 20) k
= 15 j - 38 k
Final Result
- Thus, the angular momentum L about the origin is:
L = 15 j - 38 k
This represents the angular momentum vector in terms of its components along the j and k axes.
Position Vector
- The position vector r of the mass is given as:
r = 3 i + 4 j
Velocity Vector
- The velocity vector v of the mass is:
v = 5 i - 6 j
Angular Momentum Formula
- The angular momentum L about the origin is calculated using the formula:
L = r × p
where p is the linear momentum, given by p = mv.
Since the mass m = 1, p = v.
Calculating Linear Momentum
- Therefore, the linear momentum p is:
p = 5 i - 6 j
Cross Product Calculation
- Now, we calculate the cross product of r and p:
L = r × p
= (3 i + 4 j) × (5 i - 6 j)
- Using the determinant method, we set up the matrix:
| i j k |
| 3 4 0 |
| 5 -6 0 |
- The determinant yields:
L = (0 - 0) i - (0 - 15) j + (-18 - 20) k
= 15 j - 38 k
Final Result
- Thus, the angular momentum L about the origin is:
L = 15 j - 38 k
This represents the angular momentum vector in terms of its components along the j and k axes.
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A unit mass at position vector r = 3 ICAP + 4 j cap is moving with velocity v is equals to 5 ICAP minus 6 j cap what is the angular momentum of the body about the origin?
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A unit mass at position vector r = 3 ICAP + 4 j cap is moving with velocity v is equals to 5 ICAP minus 6 j cap what is the angular momentum of the body about the origin? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A unit mass at position vector r = 3 ICAP + 4 j cap is moving with velocity v is equals to 5 ICAP minus 6 j cap what is the angular momentum of the body about the origin? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A unit mass at position vector r = 3 ICAP + 4 j cap is moving with velocity v is equals to 5 ICAP minus 6 j cap what is the angular momentum of the body about the origin?.
A unit mass at position vector r = 3 ICAP + 4 j cap is moving with velocity v is equals to 5 ICAP minus 6 j cap what is the angular momentum of the body about the origin? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A unit mass at position vector r = 3 ICAP + 4 j cap is moving with velocity v is equals to 5 ICAP minus 6 j cap what is the angular momentum of the body about the origin? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A unit mass at position vector r = 3 ICAP + 4 j cap is moving with velocity v is equals to 5 ICAP minus 6 j cap what is the angular momentum of the body about the origin?.
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