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.
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12.1 Momentum
12.2 Force is the Rate of Change of Momentum
12.3 Angular Momentum
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.
p = m v
Momentum
(kg m/sec)
Velocity (m/sec)
Mass (kg)
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.
orinelastic.
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.
12.1 Collisions in 2 and 3 Dimensions
12.1 Momentum
12.2 Force is the Rate of Change of Momentum
12.3 Angular Momentum
Investigation Key Question:
How are force and momentum related?
F = D p
D t
The relationship between force and motion follows directly from Newton's second law.
Force (N)
Change in momentum
(kg m/sec)
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 p
To find the impulse, you rearrange the momentum form of the second law.
Impulse (N•sec)
Change in
momentum
(kg•m/sec)
Impulse can be expressed in kg•m/sec (momentum units) or in N•sec.
12.1 Momentum
12.2 Force is the Rate of Change of Momentum
12.3 Angular Momentum
Investigation Key Question:
How does the first law apply to rotational motion?
L = Iw
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
(kg m2)
Angular
momentum
(kg m/sec2)
Angular
velocity
(rad/sec)
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.
Jet Engines