1. Momentum Crashing Cars Water on Walls Hitting Tennis Balls Watching Skaters Fall

2. Newton’s Second Law, Redux We have written ∑F = ma as Newton’s 2 nd. Newton: where p = mv: momentum Note if ∑F = 0, then Δp = 0. Since Δp = p f – p i = 0, this means p f = p i and momentum is conserved.

3. Conservation of Momentum In a collision between two objects, we can say that ∑F = 0 if the only force on object one is from object two, and likewise the only force on object two is from object one. Then, Newton’s third law demands that these forces add up to zero, and momentum is conserved.

4. Simple example: inelastic collision Car 1 (400 kg) moves to the right at 20 m/s; Car 2 (600 kg) moves to the left at 10 m/s. The cars collide and stick together. What happens? Only force on car 1 is from car 2, and vice versa, so momentum is conserved. p i = (400 × 20) – (600 × 10) = 2000 kg m/s. p f = (600 + 400) × V f = p i = 2000 => V f = 2.0 m/s

5. Collision Definitions  Perfectly inelastic: objects collide and stick together.  Inelastic: objects collide, don’t stick together, but collision is not elastic.  Elastic: objects collide, and kinetic energy is conserved [more on this (much) later].

6. Other momentum stuff: Impulse Although momentum is probably most often used in the conservation of momentum theorem, it is also useful in situations where ∑F ≠ 0 so that Δp = ∑F × Δt. We’ll only consider one force, so Δp = F Δt, or Change in momentum = Impulse

7. Impulse example A 20 gram tennis ball is moving to the right at 30 m/s; it is hit so that it moves to the left at 25 m/s. The ball is in contact with the tennis racket for 10 ms. What is the average force on the ball while in contact with the racket? See board for the “real world” situation, and our solution.

8. Moving Masses We use with constant mass We could also use This is useful for calculating the force on moving masses of bulk material: see board for example.

9. Qualitative issue Δp = F Δt can be used to qualitatively analyze some situations. A car is going to crash: big Δp for car, and more importantly, for driver. Two choices: Big F, small Δt or... Small F, big Δt. Which would YOU want?

10. Examples  Bridge abutments  Airbags  metal vs. rubber hammer

11. Angular Momentum Just as Linear Momentum is the product of mass and velocity, angular momentum is the product of moment of inertia and angular momentum. L = Iω

12. Conservation of Angular Momentum Just as Linear Momentum is conserved if the sum of the external forces is zero, Angular momentum is conserved if the sum of the external torques is zero. L i = L f gives I i ω i = I f ω f see the board, and maybe a demo ???