Chapter 12: Momentum. 12.1 Momentum 12.2 Force is the Rate of Change of Momentum 12.3 Angular Momentum. Chapter 12 Objectives. Calculate the linear momentum of a moving object given the mass and velocity. Describe the relationship between linear momentum and force.
Calculate the linear momentum of a moving object given the mass and velocity.
Describe the relationship between linear momentum and force.
Solve a one-dimensional elastic collision problem using momentum conservation.
Describe the properties of angular momentum in a system—for instance, a bicycle.
Calculate the angular momentum of a rotating object with a simple shape.
Investigation Key Question:
What are some useful properties of momentum?
Two balls with the same mass and speed have the same kinetic energy but opposite momentum.
A car is traveling at a velocity of 13.5 m/sec (30 mph) north on a straight road. The mass of the car is 1,300 kg. A motorcycle passes the car at a speed of 30 m/sec (67 mph). The motorcycle (with rider) has a mass of 350 kg. Calculate and compare the momentum of the car and motorcycle.
If you throw a rock forward from a skateboard, you will move backward in response.
Two 0.165 kg billiard balls roll toward each other and collide head-on.
Initially, the 5-ball has a velocity of 0.5 m/s.
The 10-ball has an initial velocity of -0.7 m/s.
The collision is elastic and the 10-ball rebounds with a velocity of 0.4 m/s, reversing its direction.
What is the velocity of the 5-ball after the collision?
(0.165 kg) v3 + (0.165 kg) (0.4 m/s)
A train car moving to the right at 10 m/s collides with a parked train car.
They stick together and roll along the track.
If the moving car has a mass of 8,000 kg and the parked car has a mass of 2,000 kg, what is their combined velocity after the collision?
(8,000 + 2,000 kg)
v3= 8 m/s
The train cars moving together to right at 8 m/s.
How are force and momentum related?12.2 Force is the Rate of Change of Momentum
F = D p
D t12.2 Force and Momentum Change
The relationship between force and motion follows directly from Newton's second law.
Change in momentum
Change in time (sec)
Starting at rest, an 1,800 kg rocket takes off, ejecting 100 kg of fuel per second out of its nozzle at a speed of 2,500 m/sec. Calculate the force on the rocket from the change in momentum of the fuel.
F D t = D p12.2 Force and Momentum Change
To find the impulse, you rearrange the momentum form of the second law.
Impulse can be expressed in kg•m/sec (momentum units) or in N•sec.
How does the first law apply to rotational motion?Inv 12.3 Angular Momentum
L = Iw12.3 Calculating angular momentum
Angular momentum is calculated in a similar way to linear momentum, except the mass and velocity are replaced by the moment of inertia and angular velocity.
Moment of inertia
An artist is making a moving metal sculpture. She takes two identical 1 kg metal bars and bends one into a hoop with a radius of 0.16 m. The hoop spins like a wheel. The other bar is left straight with a length of 1 meter. The straight bar spins around its center. Both have an angular velocity of 1 rad/sec. Calculate the angular momentum of each and decide which would be harder to stop.