Atlas MCAT Course
Equations & How to Use Them → Equations: Motion
Equations: Motion
Forces, momentum, circles, and rotation.
01The idea
This part of the course collects the equations and, more importantly, when to use each one. Start with the situation, not the formula.
THREAD · Structure → function
02Build the model
ANewton’s second law: how forces create acceleration
Use when: velocity is changing; an object is speeding up, slowing down, or turning; you care about why motion is changing.
Passage cues: “Net force”, “Acceleration”, “Frictionless surface”, “Mass increased/decreased”.
Don’t use it for: constant velocity (no acceleration); pure energy comparisons without forces.
BKinematics (constant acceleration): describing motion without asking why
Use when: acceleration is constant; you’re given time, distance, velocity; forces are irrelevant or unnecessary.
Passage cues: “Starts from rest”, “After 3 seconds”, “Travels a distance of…”.
Don’t use it for: variable acceleration; rotational motion; force analysis questions.
CMomentum: how much motion an object has
Use when: objects collide or recoil; conservation language appears; velocity and mass matter.
Passage cues: “Collision”, “Recoil”, “Explosion”, “Before and after interaction”.
Don’t use it for: pure energy questions; situations with large external forces over time.
DConservation of momentum: motion is exchanged, not destroyed
Use when: collisions occur over very short times; external forces are negligible; systems are isolated.
Passage cues: “Isolated system”, “Negligible external forces”, “Collision time is very short”.
Don’t use it for: long-duration forces (friction over time); non-isolated systems.
EElastic vs. inelastic collisions: whether kinetic energy is conserved
| Collision | Conserved |
|---|---|
| Elastic | Momentum and kinetic energy |
| Inelastic | Momentum only (perfectly inelastic: objects stick together) |
Use when: the collision type is specified; objects stick, bounce, or deform.
FImpulse: how force changes momentum
Use when: force acts over a short time; airbags, padding, helmets appear; you’re asked how to reduce injury.
Passage cues: “Impulse”, “Collision time”, “Force spread out”.
Don’t use it for: steady forces over long distances (use work–energy).
GCentripetal acceleration and force: why circular motion requires force
Use when: motion is circular or curved; speed is constant but direction changes; tension, gravity, or friction causes circular motion.
Passage cues: “Uniform circular motion”, “Radius”, “Turns / orbits”.
HNewton’s law of gravitation: why masses attract
Use when: planets, satellites, or large masses interact; distance dependence matters.
Passage cues: “Orbital”, “Gravitational attraction”, “Inverse square”.
Don’t use it for: small-scale lab objects (gravity negligible).
IGravitational potential energy: energy stored due to separation
Use when: orbits or separation distance changes; energy-based gravity questions.
JTorque: the rotational effect of a force
Use when: objects rotate about a pivot; lever arms, hinges, joints appear; balance and rotation are discussed.
Passage cues: “Pivot point”, “Lever arm”, “Rotational equilibrium”.
Don’t use it for: pure linear motion; problems where the force acts at the pivot.
KRotational equilibrium, inertia, and dynamics: why objects do or don’t rotate
Use when: systems are balanced (seesaws, joints, beams); torque causes rotational acceleration (conceptual cause–effect).
03See the connections
The lesson names these links itself. Read the map left to right.
Why motion changes
- F = ma
- Kinematics (no causes)
Interactions
- Momentum, conservation
- Impulse
- Collisions
Curves and rotation
- Centripetal, gravitation
- Torque, τ = Iα
Next: energy equations.
04Reason with it
Four questions. Answer in your head first, then choose. You’ll see the reasoning either way.
Think first.
A passage gives an object’s starting speed, constant acceleration, and time, and asks how far it travels. No forces are mentioned. Which tool first?
Think first.
Why does an airbag reduce injury in a crash?
Think first.
Two carts collide and stick together on a frictionless track. What is conserved?
Think first.
A satellite’s distance from Earth’s center doubles. What happens to the gravitational force on it?
05MCAT lens
MCAT shortcuts
Changing velocity → forces must be involved
No forces mentioned → kinematics first
No outside push → momentum conserved
Increase time → decrease force
Turning = accelerating
Farther from pivot → more torque
06Common traps
Trap 1: Use F = ma whenever something moves
Misconception
Constant velocity means no net force.
Correct model
Use F = ma when velocity changes.
Trap 2: Momentum is only conserved in elastic collisions
Misconception
All collisions conserve momentum.
Correct model
Only elastic collisions also conserve kinetic energy.
Trap 3: Constant speed in a circle means no acceleration
Misconception
Direction is changing.
Correct model
Turning = accelerating.
07Dependency check
Can you reconstruct this concept without looking at the page? You should now be able to reason through:
When to use F = ma vs kinematics
Check against 02 · A and B: causes vs description.
When momentum is conserved
Check against 02 · C and D: isolated systems, short collisions.
How impulse reduces force
Check against 02 · F: longer time, smaller force.
What torque depends on
Check against 02 · J and K: force, lever arm, angle.
If something feels unclear, the missing idea is usually thisIdentify what is happening first; the equation follows.
08Remember
REMEMBER · if you keep only a few things
- F_net = ma: only when velocity changes.
- Kinematics: constant acceleration, no causes.
- p = mv; momentum conserved in every collision.
- J = FΔt = Δp: longer time, smaller force.
- a_c = v²/r; F = Gm₁m₂/r².
- τ = rF sin θ; Στ = 0 means no rotation.
09Forward hook
Mechanics also has an energy side, which often solves problems faster.
When should you track energy instead of forces?
That leads to the energy equations.
Next lessonEquations: Energy→