Physics: Mechanics and Energy

Mechanics is the backbone of the MCAT Chem/Phys section. Most items are not brute calculations but conceptual questions dressed in a passage: identify the right principle (a conservation law, a free-body diagram, or the work-energy theorem) and the answer usually falls out with minimal math. Learn the frameworks below and you can solve the physics block quickly and reliably.

Core Idea

• Vectors have direction; scalars do not. Displacement, velocity, acceleration, force, and momentum are vectors; distance, speed, mass, time, and energy are scalars. Getting this right prevents most sign errors.
• Conservation laws are shortcuts. When a quantity (energy or momentum) is conserved, you compare "before" and "after" without tracking every step in between.
• Free-body diagrams turn word problems into equations. Draw every force, resolve into components, and apply Newton's second law axis by axis.

Kinematics

Kinematics describes motion without asking what causes it. For constant acceleration, the key equations are v = v0 + at, x = x0 + v0t + (1/2)at^2, and v^2 = v0^2 + 2a(delta x). Velocity is the rate of change of displacement; acceleration is the rate of change of velocity. A common MCAT theme is that speeding up, slowing down, or changing direction all count as acceleration because velocity is a vector.

For projectile motion, treat the horizontal and vertical axes independently. Horizontal velocity is constant (no horizontal force, ignoring air resistance); vertical motion has constant downward acceleration g ~ 9.8 m/s^2. At the peak of the trajectory the vertical velocity is zero, but the horizontal velocity and the acceleration g are unchanged.

Newton's Laws and Forces

• First law (inertia): an object keeps its velocity unless a net external force acts. Equilibrium means net force = 0, not necessarily zero velocity.
• Second law: F_net = ma. Net force and acceleration point the same direction; larger mass means smaller acceleration for a given force.
• Third law: forces come in equal-and-opposite pairs acting on different objects. The pair never cancels on a single object because they act on two bodies.

Common forces: gravity (weight = mg, always downward), the normal force (perpendicular to a surface, not always equal to mg), friction (f = mu N, opposing relative motion; static friction can range from 0 up to a maximum), and tension (pulls along a rope). Torque (tau = rF sin theta) produces rotation; an object is in full equilibrium only when both net force and net torque are zero.

Work and Energy

Work transfers energy: W = Fd cos theta, where theta is the angle between force and displacement. A force perpendicular to motion (like the normal force or centripetal force) does zero work. Kinetic energy is KE = (1/2)mv^2; gravitational potential energy near Earth is PE = mgh.

The work-energy theorem states that net work equals the change in kinetic energy: W_net = delta KE. When only conservative forces act, mechanical energy is conserved: KE_i + PE_i = KE_f + PE_f. Nonconservative forces such as friction remove mechanical energy (usually as heat). Power is the rate of doing work: P = W/t = Fv.

Momentum and Collisions

Momentum p = mv is always conserved for an isolated system (no external net force). Impulse equals the change in momentum: J = F(delta t) = delta p, which is why airbags and follow-through lengthen contact time to reduce force. In an elastic collision, both momentum and kinetic energy are conserved. In an inelastic collision, momentum is conserved but kinetic energy is not; in a perfectly inelastic collision the objects stick together and move with one common velocity.

High-Yield Exam Patterns

• Choose the conservation law first. If heights and speeds are asked, use energy conservation; if two objects interact/collide, use momentum conservation.
• Perpendicular forces do no work — normal force, tension on a circular path, and centripetal force are classic zero-work traps.
• Projectile questions hinge on treating x and y separately; horizontal velocity never changes.
• Impulse questions reward the insight that a longer contact time lowers the peak force for the same momentum change.
• Kinetic energy scales with v^2, so doubling speed quadruples KE and stopping distance — a favorite twist.

Common Traps to Avoid

• Treating the normal force as always equal to mg (it changes on inclines, in elevators, or with an applied vertical force).
• Thinking Newton's third-law pairs cancel — they act on different objects and never cancel.
• Assuming kinetic energy is conserved in every collision; it is conserved only in elastic collisions.
• Forgetting the cos theta in work, so a force at an angle is over-counted.
• Confusing scalars and vectors, especially calling constant-speed circular motion "no acceleration."