Angular momentum of a particle with a symmetrical path

AI Thread Summary
The discussion focuses on calculating the angular momentum of a projectile launched at an angle θ in a gravitational field. At the origin, the angular momentum is zero due to the absence of a position vector (r). For the highest point of the trajectory, the perpendicular distance from the origin to the velocity vector is the maximum height of the projectile. The angular momentum can be expressed as mvr_perpendicular, where v is the velocity and r_perpendicular is the distance from the origin to the velocity vector. Understanding the relationship between the position vector and the momentum vector is crucial for solving the problem.
doneky
Messages
13
Reaction score
0

Homework Statement


A projectile of mass m is launched with an initial velocity [PLAIN]https://www.webassign.net/images/boldv.gif[I]i[/I] making an angle θ with the horizontal as shown below. The projectile moves in the gravitational field of the Earth. Find the angular momentum of the projectile about the origin when the particle is at the following locations. (Use the following as necessary: vi, θ, m, and g for the acceleration due to gravity.)
11-p-019.gif

(a) at the origin
(b) at the highest point of its trajectory
(c) just before it hits the ground

Homework Equations


L=r x p

The Attempt at a Solution


For (a) angular momentum is zero because there is no r.

I mean, the problem overall seems easy, but how on Earth do I find r for the other two positions? The answer doesn't help with how this is found at all. Is there some sort of property or formula with symmetrical projectile motion?
 
Last edited by a moderator:
Physics news on Phys.org
Given that you abandoned the last thread you started, not even acknowledging the response, it seems unlikely that anybody would be motivated to help you with this one.
 
I asked that question and then went to bed. Then I started reviewing every other chapter and have been doing solely that, so I apologize, since that problem had been pretty much the least of my worries.
I was literally planning on replying to that thread once I reached that chapter. This is the chapter prior to that one.
 
Since the angular momentum depends on then cross product of the position vector and momentum vector(which is in the same direction as velocity),the formulae for the angular momentum maybe written as mvrperpendicular. (The cross product of the component of r vector along/parallel to velocity/momentum is 0)
Find the perpendicular distance of the velocity vector from the origin.for eg in the first case it is 0 since the velocity vector passes through the origin and in the second case it is the max height of the projectile.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...

Similar threads

Back
Top