Confusion with Impulse and Work I get Momentum and Impulse as well as Work and energy but struggle when it comes to connecting the two ideas. I understand that an objects KE can change without its momentum changing, Like in a inelastic collision were the KE of the system decreases but the amount of matter moving to left with some speed - the amount of matter moving to the right with some speed will be equal before and after the collision. Hence Momentum is Conserved. My confusion starts with the question is an impulse of a force on an object always accompanied by some work done on the object by that force?
 A: Impusle is a property defined as: $$\vec{I} = \int \sum \vec{F}.dt$$
and by virtue of this definition, it need not always be accompanied by work.
Consider an example of you standing on a skateboard and pushing on a wall setting yourself in motion away from the wall.
In this case, the force from the wall on your hands moves through no displacement; the force is always located at the interface between the wall and your hands. Hence, no work is done on the system of you and the skateboard. (The resulting kinetic energy however comes from the potential energy stored in your body).
The impulse-momentum theorem will suggest that: $$\Delta \vec p_{tot} = \vec I = m \Delta \vec v = \int \vec F_{\text{wall}}.dt$$ where $\vec F_{\text{wall}}$ is the force exerted by the wall on your hands. Hence, the impulse does not result in a work.
Hope this helps.
A: The standard example of a force doing no work is when an object is moving in a circle at constant speed - the force points towards the centre of the circle. Over 180 degrees there is a non-zero impulse; the direction of movement has changed so the momentum vector has changed. However the speed has not changed, so no work has been done.
It is actually impossible to change the kinetic energy of a single object without changing its momentum, because if you change the kinetic energy you must change the velocity. In an interaction between more than one object the total momentum stays fixed though, even if the total kinetic energy changes.
