Angular Momentum multiplication

In summary, at a particular instant, the location of an object relative to location A is given by the vector A = < 7, 6, 0 > m. The momentum of the object at this instant is p = < 20, 8, 0 > kg · m/s. To find the angular momentum of the object about location A, you would need to multiply r*p with r perpendicular from the location to the line of motion. However, to find r perpendicular, you may need to use the cross product of two vectors and the definition of angular momentum in terms of a cross product.
  • #1
cowmoo32
122
0
At a particular instant the location of an object relative to location A is given by the vector A = < 7, 6, 0 > m. At this instant the momentum of the object is p = < 20, 8, 0 > kg · m/s. What is the angular momentum of the object about location A?

According to my book, angular momentum is found by multiplying r*p with r perpindicular from the location to the line of motion. how do I find r perpindicular?
 
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  • #2
cowmoo32 said:
At a particular instant the location of an object relative to location A is given by the vector A = < 7, 6, 0 > m. At this instant the momentum of the object is p = < 20, 8, 0 > kg · m/s. What is the angular momentum of the object about location A?

According to my book, angular momentum is found by multiplying r*p with r perpindicular from the location to the line of motion. how do I find r perpindicular?
Does your book say anything about the cross product of two vectors and the definition of angular momentum in terms of a cross product?
 
  • #3


To find the perpendicular distance from location A to the line of motion, we can use the cross product between the vector A and the momentum vector p. The cross product of two vectors results in a vector that is perpendicular to both of the original vectors. In this case, the cross product of A and p would give us a vector that is perpendicular to the plane formed by A and p.

Using the cross product, we can find the perpendicular distance as follows:

r perp = A x p

= < 7, 6, 0 > x < 20, 8, 0 >

= < 0, 0, 84 >

Therefore, the angular momentum of the object about location A would be:

L = r perp * p

= < 0, 0, 84 > * < 20, 8, 0 >

= < 0, 0, 672 > kg · m^2/s

We can also verify this result by using the formula for angular momentum, which is L = I * ω, where I is the moment of inertia and ω is the angular velocity. In this case, the moment of inertia would be the mass of the object multiplied by the square of the perpendicular distance from location A to the line of motion. So, using the same values as before, we would get:

L = m * r perp^2 * ω

= 1 * < 0, 0, 84 >^2 * < 0.4, 0, 0 >

= < 0, 0, 672 > kg · m^2/s

This confirms that our previous result is correct. In summary, to find the angular momentum of an object about a particular location, we need to find the perpendicular distance from that location to the line of motion and then multiply it by the momentum of the object. This is an important concept in understanding the rotational motion of objects and can be applied in various scientific and engineering fields.
 

Related to Angular Momentum multiplication

What is Angular Momentum multiplication?

Angular Momentum multiplication is a phenomenon in physics where the total angular momentum of a system can increase or decrease without any external torque being applied. This is due to the redistribution of angular momentum within the system.

How does Angular Momentum multiplication occur?

Angular Momentum multiplication can occur when a system experiences a change in its shape or rotation rate. This can happen due to internal forces acting on the system, such as the transfer of angular momentum between different parts of the system.

What is the significance of Angular Momentum multiplication?

Angular Momentum multiplication is significant because it allows for the conservation of angular momentum in a system, even when there are changes in its shape or rotation rate. This helps to explain the behavior of many physical systems, such as spinning tops and planets orbiting around stars.

Can Angular Momentum multiplication be observed in everyday life?

Yes, Angular Momentum multiplication can be observed in many everyday objects and phenomena. For example, when a figure skater pulls in their arms while spinning, their rotation rate increases due to the redistribution of their angular momentum. Another example is the Earth's axial tilt, which is maintained by the redistribution of angular momentum between the Earth and the Moon.

Are there any practical applications of Angular Momentum multiplication?

Yes, there are several practical applications of Angular Momentum multiplication. One example is the use of gyroscopes in navigation systems, which rely on the conservation of angular momentum to maintain their orientation. Another example is the use of centrifuges in laboratories, which use Angular Momentum multiplication to separate materials based on their density.

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