Impulse of a force - effect on linear and angular momentum

[Froskoy]

Hi,

I'm having trouble understanding what the relation is between the impulse of a force during a collision and the changes in linear and angular momentum during the collision.

I know that the principle of conservation of linear momentum says that the total linear momentum before is equal to the total linear momentum after and the principle of conservation of angular momentum states that the total angular momentum before is equal to the total angular momentum after, but am struggling with the interpretation of this.

Do these principles mean that

1) the sum of the impulse + linear momentum before + angular momentum before = linear momentum before + angular momentum after

OR

2) (the sum of impulse + linear momentum before = linear momentum after) AND ALSO (the sum of impulse + angular momentum before = angular momentum after)?

With very many thanks,

Froskoy.

 

[tiny-tim]

Hi Froskoy!

Linear momentum and angular momentum can't be added.

(for a start, linear momentum is a vector, but angular momentum is a pseudovector!)

it's 3) … (the sum of impulse + linear momentum before = linear momentum after) AND ALSO (the sum of torque (or moment) of impulse + angular momentum before = angular momentum after)

 

[morrobay]

There is no substitute for a good Physics text. Following from Halliday - Resnick
p₂ - p₁ = integral 1>2 dp = integral 1>2 Force dt = Impulse

The integral of force over the time interval during which force acts is called the
impulse of the force and is equal to the change in momentum. Both the impulse
and linear momentum are vectors and have same units and dimensions.
And is area under force time curve.
integral t₁>t₂ Force dt

 

[Froskoy]

Thanks very much! It all makes a lot more sense now!

 

[PJC01]

Hi Froskoy,

The impulse of a force during a collision does indeed have an effect on both linear and angular momentum. The principles of conservation of linear momentum and conservation of angular momentum are both fundamental laws of physics that describe the behavior of objects in motion.

To answer your question, the correct interpretation is option 2. The impulse of a force during a collision will result in changes to both linear and angular momentum. This means that the sum of the impulse and the initial linear momentum will be equal to the final linear momentum, and the sum of the impulse and the initial angular momentum will be equal to the final angular momentum.

To understand this better, let's break it down. The impulse of a force is the change in momentum of an object, and is equal to the force multiplied by the time it acts on the object. So, during a collision, the impulse of the force will cause a change in the object's momentum. This change can be in the form of a change in direction, speed, or both.

Linear momentum is a measure of an object's motion in a straight line, while angular momentum is a measure of an object's rotation around a fixed point. During a collision, the impulse of a force can cause changes in both of these types of motion. For example, if a ball is hit with a bat, the impulse of the force will cause a change in the ball's linear momentum as it moves in a different direction. At the same time, the bat's force will also cause a change in the ball's angular momentum as it starts to rotate.

So, to summarize, the impulse of a force during a collision will result in changes to both linear and angular momentum. The principles of conservation of linear momentum and conservation of angular momentum ensure that the total momentum of the system (object or objects involved in the collision) remains constant before and after the collision. This means that the sum of the impulse and the initial momentum will be equal to the final momentum in both linear and angular directions.

I hope this helps to clarify your understanding. Keep exploring and questioning, that's what science is all about!

Best,