Unit 1 - 3 Class Notes

Why is mass inconsequential to falling in the absence of air resistance (so the rate of acceleration for all objects is the same, regardless of weight)?

Because the gravitational force pulling down an object increases with its mass, but so does its resistance to acceleration (inertia).

(So even though a 10kg object and a 1kg object are pulled by gravity with different forces, the 10kg object requires more force than the 1kg object to achieve the same acceleration)

(Think like Galileo: If heavy objects fell faster, a light object attached to a heavy object should slow it down, but the combined unit is actually heavier!)

Describe the graphs of v and x (over t) when acceleration is zero.

The position graph is linear, while the velocity graph is constant

Describe the graphs of v and x (over t) when acceleration is constant.

The position graph is quadratic, while the velocity graph is linear

What is gamma in p = m * (gamma) * v?

A limiting factor so no particle moves with infinite velocity that only significantly effects particles moving close to the speed of light (making p = mv an approximation)

When does momentum change?

When velocity changes (the object has some acceleration)

How do you determine the surroundings of a system?

Determine what objects influence the system

What is impulse?

The change in momentum or Fnet * deltat

What must occur if there has been a change in the momentum of a system?

A force must have acted on the system

Which of the properties of a harmonic oscillator does its period NOT depend on?

Its amplitude

How can you find the location of a harmonic oscillator?

Plug and chug into the analytical solution for the ideal spring-mass system

Why is the net force for an object falling at constant speed zero?

Because constant speed means constant momentum (so Fnet = 0)

Please practice deriving the kinematic equation from the momentum principle from 2/3/2026!

OK

Why is the graph of position vs time quadratic based on the kinematic equation?

Because the position is proportional to the square of time (resulting in a parabola)

What can you do to find the time when the position of an object reaches its maximum?

Use the test for maxima on its derivative (velocity, when it equals zero and all that jazz)

What part of the kinematic equation is related to Newton’s First Law? (Accounts for inertial velocity)

V0 * t

How can you tell whether two objects will hit each other?

Determine whether they are moving with the same acceleration (hit that frog with a cannon!)

Why is the acceleration of an object that’s been thrown downward always equal to the gravitational acceleration?

Because your hand only contacts it (exerts force) before it leaves your hand (but its final position is still affected by its inertial velocity!)

What is the restoring force?

The force pushing against the gravitational force of a mass on a spring, which causes harmonic motion and is proportional to the displacement from equilibrium height.

Why is Hooke’s Law negative?

Because the force points away from the mass to restore itself to its equilibrium point.

When is the spring force at its maximum?

At the maximum of the spring’s compression or stretch (allowing the spring force to dominate the gravitational force)

Please review the derivation of the equation of motion from 2/4/2026.

OK

Please review your trig formula sheet.

OK

What are action-reaction force pairs?

Forces equal in magnitude but opposite in direction and acting on different objects

List the steps to find the force of one object in a system of objects moving with the same acceleration due to one force.

Find the total acceleration with total mass, then use a force diagram to solve for the individual forces

In what direction does the normal force always point?

In the direction perpendicular to the surface

Why does a wrench appear to float in space (near the Earth)?

Because although it experiences the force of gravity downwards, it is moving very slowly and experiencing an angular momentum that makes its assumed path around the Earth an oval (less gravitational force away from the earth, more nearer to the earth, the closer it is, the more angular velocity it experiences and vice-versa)