Angular Momentum multiplication

[cowmoo32]

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?

 

[OlderDan]

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?

 

[kyle8921]

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.