AP PHYSICS unit 4

What is linear momentum?

A measure of motion: mass multiplied by velocity

What is the equation for momentum?

p = mv

What are the units of momentum?

kg·m/s

Is momentum a scalar or vector?

Vector; it has magnitude and direction

What determines momentum’s direction?

The direction of velocity

What is an object’s momentum at rest?

Zero, because velocity is zero

What does negative momentum mean?

Motion in the chosen negative direction

What happens to momentum if mass doubles while velocity stays constant?

Momentum doubles

What happens to momentum if velocity doubles while mass stays constant?

Momentum doubles

What is the change in momentum?

Final momentum minus initial momentum

What is the equation for change in momentum?

Δp = p_f − p_i = m(v_f − v_i), for constant mass

What is impulse?

The effect of a force acting over time

What is the impulse-momentum theorem?

Net impulse equals change in momentum: J = Δp

What is the impulse equation for a constant net force?

J = F_net Δt

What are the units of impulse?

N·s, equivalent to kg·m/s

What is the average net force equation?

F_avg = Δp / Δt

What is Newton’s second law in momentum form?

F_net = dp/dt

How do you calculate impulse from a force-time graph?

Find the signed area under the net force-time graph

What does area above the force-time axis represent?

Positive impulse

What does area below the force-time axis represent?

Negative impulse

How do you find impulse for a variable force?

J = ∫ F_net(t) dt over the time interval

Why can a longer stopping time reduce average force?

For the same momentum change, increasing time decreases average force

What happens to momentum when velocity reverses?

Momentum reverses direction, too

What is the biggest sign mistake in momentum problems?

Giving opposite directions the same sign

What does conservation of momentum mean?

Total system momentum stays constant when net external impulse is zero

What is the two-object momentum conservation equation?

m₁v₁ᵢ + m₂v₂ᵢ = m₁v₁f + m₂v₂f

What does the symbol Σ mean?

Sum; add the relevant quantities

What is a system in physics?

The object or collection of objects being analyzed

What are internal forces?

Forces between objects within the chosen system

What are external forces?

Forces exerted on the system from outside it

When is momentum conserved?

When the net external impulse on the system is zero.

Do internal forces change the total momentum of an isolated system?

No; internal forces cannot change its total momentum

Can individual objects change momentum during a collision?

Yes; their individual momenta can change while total momentum stays constant.

What is the first step in a momentum conservation problem?

Define the system and choose a positive direction

What happens when two objects initially at rest push apart?

Their momenta are equal in magnitude and opposite in direction

What is the total momentum of a system initially at rest?

Zero, if all objects in the system are at rest.

What is a collision?

A short interaction in which objects exert forces on one another

What is an elastic collision?

A collision that conserves both momentum and total kinetic energy.

What is an inelastic collision?

A collision that conserves momentum but not total kinetic energy, assuming negligible net external impulse.

What is a perfectly inelastic collision?

A collision in which the objects stick together

Is momentum conserved in an elastic collision?

Yes, if net external impulse is zero

Is kinetic energy conserved in an elastic collision?

Yes, total kinetic energy is conserved

Is kinetic energy conserved in an inelastic collision?

No; some kinetic energy transforms into other forms.

Is momentum conserved in a perfectly inelastic collision?

Yes, if net external impulse is zero.

What is the key feature of a perfectly inelastic collision?

The objects move together after the collision.

What is the final velocity when two objects stick together?

v_f = (m₁v₁ᵢ + m₂v₂ᵢ) / (m₁ + m₂)

Why do you add the masses in a perfectly inelastic collision?

The objects move together as one combined mass.

Can kinetic energy decrease during a collision?

Yes; in inelastic collisions, some becomes thermal energy, sound, or deformation.

Can total energy be conserved even when kinetic energy is not?

Yes; energy can transform into other forms.

What two quantities are conserved in an elastic collision?

Total momentum and total kinetic energy

What is the equation for total kinetic energy?

K = ½mv²

What is the momentum equation for a two-object collision?

m₁v₁ᵢ + m₂v₂ᵢ = m₁v₁f + m₂v₂f

What is the kinetic energy equation for an elastic collision?

½m₁v₁ᵢ² + ½m₂v₂ᵢ² = ½m₁v₁f² + ½m₂v₂f²

In a one-dimensional elastic collision, what is the relative velocity relationship?

v₁ᵢ − v₂ᵢ = −(v₁f − v₂f)

In a one-dimensional elastic collision between equal masses, what often happens if one object is initially at rest?

The moving object can stop while the initially resting object moves off with its velocity.

In a one-dimensional elastic collision between equal masses, what often happens if one object is initially at rest?

The moving object can stop while the initially resting object moves off with its velocity.

What is a common mistake when using momentum conservation?

Ignoring direction and using incorrect signs.

How should you handle objects moving in opposite directions?

Choose a positive direction; assign opposite signs to opposite velocities.

Is speed the same as velocity in momentum equations?

No; velocity includes direction, while speed is magnitude only.

What is a common mistake with kinetic energy?

Forgetting to square the speed: K = ½mv²

Can you conserve kinetic energy in every collision?

Back: Signs, units, conservation assumptions, and whether the result makes physical sense

No; only in elastic collisions.

What is a common mistake when objects stick together?

Using separate final velocities instead of one shared final velocity

What should you do if an object rebounds?

Reverse the sign of its final velocity if it reverses direction

What is the best general strategy for collision problems?

Define the system, choose a positive direction, write conservation equations, then solve.

What should you check after solving a momentum problem?

Signs, units, conservation assumptions, and whether the result makes physical sense