Physics 30 Unit 1 - Momentum and Impulse

04/03/26

inertia

• This is an object's resistance to changes in its motion.

• directly related to mass: the greater the mass, the greater the inertia.

• Inertia explains why an object at rest stays at rest, and an object in motion stays in motion unless acted upon by an external force (Newton's First Law).

• applies even to objects at rest

• describes changes in motion

• “the tendency of a body to oppose a change in its position”

momentum

• Momentum is a vector quantity equal to the product of an object's mass and velocity (p = mv).

• It represents the motion of the object

• depends on the mass and velocity of the object

• units of Kg(m/s) or Ns

• formula is p = m x Δv orrrr p = F x Δt

how are momentum and inertia different?

momentum describes the motion of an object, while inertia describes the object’s changes in motion

for graph questions, how do we know what slope means?

in the case of p = mv, slope represents whatever the “unnamed” variable is on the graph. if you see p and v as the y and x axes of a graph, the only thing left is the mass of the object, which will be your slope.

newton’s first law

objects at rest stay at rest and objects in motion stay in motion, unless acted upon by an outside (unbalanced) force. this is called the law of inertia, as inertia describes this property

impulse

• the product of the net force and the time the force acts on the object

• impulse causes a change in the momentum of an object, so the object’s momentum will change in the direction of the applied force

• represented by F x Δt = m Δv

applications of impulse and momentum

by increasing the amount of time it takes to change the impulse of an object, the force experienced by the object is lowered. in reference to sudden stops, we know that an object hitting another will have the hit object exert an equal and opposite force on the og object. so, by lowering the force the og object hits the hit object with (by increasing time), the hitting object experiences less force overall.

we apply this in making cars safer. by adding crumple zones/airbags/seatbelts, we increase the time for the impulse, lowering overall force experienced by the passengers, and keep them safer, as whatever they run into exerts less force on them in return

force-time graphs

• the y-axis is Force in Newtons (be careful of units! check them!)

• the x-axis is Time in seconds (be careful of units! check them!)

• F x t = P

• the area under the curve is impulse (P)

to solve:

1. find the area of each portion of the graph, may need to split it into rectangles and triangles

   1. this is your total impulse

2. you’ll likely be asked to find the final speed, so you’ll divide the impulse by the mass of the object

3. NOTE: you’ve only found the change in velocity (ΔV) and they will try to trick you with this!!!

4. from there, just manipulate ΔV = V_f - V_i to find the speed they want

fuckass graph units explanations

see how it has (10² N) as its units? it means that for whatever y-value the line is at (example is 20), is (y-value) x 10² Newtons

in this case, that’d be 20 × 10² Newtons of force

what kinds of systems are there?

• open

• closed

• isolated

open systems

mass may enter or leave the system and external forces may influence the system

closed systems

no mass enters or leaves the system

isolated systems

no external forces act on the system, and no energy leaves the system. the only net forces acting on the objects in the system are the forces that the objects exert on each other.

what kinds of systems do we assume for conservation of momentum questions?

• we assume a closed, isolated system (no mass enter/leave, no energy enter/leave, no external forces)

• collisions are examined immediately before and after to prevent any external force like friction or gravity from becoming significant

• only the internal forces in the system are significant (ignore friction/gravity when doing these questions, until you’re asked for kinematics)

newton’s third law

• every force has an equal and opposite reactionary force

• while the momentum of objects in the system may change, the total amount of momentum is conserved (in isolated systems)

what types of interactions are possible

• collision: bounce

• collision: stick

  • always inelastic

  • remember to add masses

• explosions

stick collisions are always what?

inelasticccccc

elastic collisions

collisions where both energy and momentum are conserved. purely ___ collisions are hard to produce in the ordinary world because there is always energy converted into heat, sound, deformation, or some other form of energy

inelastic collisions

when momentum is conserved, but kinetic energy is not. most collisions are ____, since some energy is lost to other forms. when objects hit and stick together, the collisions are called totally inelastic

how can momentum always be conserved but not kinetic energy?

because of N3L, the force transfer within any collision is equal and opposite, so momentum will always be conserved because there is never a force change

but, kinetic energy can change because velocity (as calculated from momentum) is impacted by the mass of the object. when the energy that created a specific velocity is transferred into an object with a different mass, that same energy translates to a different speed. as the kinetic energy formula includes speed, the change in velocity means a change in kinetic energy

for 2D conservation of momentum, what do i have to remember?

• the angle they give you will likely be inside the triangle.

• angles on the inside are mirrored on the outside if they share an arm

• if they ask for an angle in a specific orientation, then you may need to subtract it from 90