# Linear/angular Momentum / tripping / conservation

• timarli
In summary, the conversation discusses the scenario of a rectangular object sliding on a frictionless horizontal surface, with a certain speed and height, colliding with an obstacle of a different height. The question is raised about the relation between linear momentum, angular momentum, and conservation of momentum in this situation. Different approaches are suggested, with the final conclusion being to use angular momentum and choose a reference point that makes the unknown impulse have zero moment in order to solve for the speed at which the object will trip.
timarli

## Homework Statement

An rectangular object(mass m) sliding on a horizontal plane (surface is frictionless), with a speed V, object height H.
then hits a rectangular obstacle with height h. V is large enough to cause tripping

## Homework Equations

what is the relation between linear momentum / angular momentum / conservation of momentum

## The Attempt at a Solution

is this what's happening; the object has a momentum of P=mV.
then an impulse I=t*F is applied to the object by the obstacle.
This impulse reduces the linear momentum to P'=m*V-F*x
---This m*V-Fx gives the angular momentum(with respect to the point of contact) causing the rotation?---

I am not sure if my thinking is correct, especially my last statement.

An alternative is; taking initial mV as an angular momentum with changing radius wrt the contact point? ie not mentioning linear momentum at all?

timarli said:
is this what's happening; the object has a momentum of P=mV.
then an impulse I=t*F is applied to the object by the obstacle.
It won't be useful to introduce F or t. Just leave it as I.
This impulse reduces the linear momentum to P'=m*V-F*x
x?
---This m*V-Fx gives the angular momentum(with respect to the point of contact) causing the rotation?---
I provides the angular momentum.
To solve the problem, you need to use a fact concerning subsequent motion of the block.. like, some point that is stationary immediately after impact.

haruspex said:
It won't be useful to introduce F or t. Just leave it as I.

x?

I provides the angular momentum.
To solve the problem, you need to use a fact concerning subsequent motion of the block.. like, some point that is stationary immediately after impact.

Thanks a lot haruspex.

x was wrong, well spotted. It should be 't'.

what I am trying to do is derive a formula to show the affect of speed on the tripping.

Assuming the object is a car and the obstacle is a concrete block; I would like to find out what's the speed above which the car will trip. So the top of concrete can be the reference point.

I know the mass, I know the object height and center of gravity and obstacle height. I am still struggling to figure out writing the equation. Not sure if I need to use momentum equations or energy equations.

timarli said:
Not sure if I need to use momentum equations or energy equations.
You need to pick the one that's conserved. There is an unknown impulse at the point of impact, and it clearly does not conserve work. The best, then, is to take angular momentum, picking a reference point that makes the unknown impulse have zero moment.

1 person

Your thinking is on the right track. When the object hits the obstacle, there is an impulse applied which changes its linear momentum. This change in momentum also causes a change in angular momentum, as the object will start to rotate about the point of contact with the obstacle. The change in linear momentum will be equal and opposite to the change in angular momentum, in accordance with the principle of conservation of momentum. Therefore, the total momentum (both linear and angular) of the object will remain constant throughout the collision.

## 1. What is linear momentum?

Linear momentum is a measure of an object's motion in a straight line. It is calculated by multiplying the object's mass by its velocity.

## 2. What is angular momentum?

Angular momentum is a measure of an object's rotational motion. It is calculated by multiplying the object's moment of inertia by its angular velocity.

## 3. How is momentum conserved?

Momentum is conserved in a closed system, meaning that the total momentum of all objects in the system does not change over time. This is due to Newton's third law of motion, which states that every action has an equal and opposite reaction.

## 4. What is tripping in terms of momentum?

Tripping in terms of momentum refers to an object's sudden change in motion due to an external force or interaction. This change in motion can affect an object's linear or angular momentum.

## 5. How does conservation of momentum relate to collisions?

In collisions between objects, the total momentum of the system before the collision is equal to the total momentum after the collision. This is because the forces between the objects during the collision are internal and do not change the overall momentum of the system.

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