MCAT Physics Mechanics Review

Success on the MCAT Physical Sciences section demands more than formula recall; it requires a deep, interconnected understanding of mechanics to solve complex, passage-based problems quickly and accurately. This review builds your conceptual foundation in kinematics and dynamics while honing the estimation and logical reasoning skills essential for a no-calculator exam. Mastering these principles is also your first step toward understanding biomechanics, cardiovascular flow, and physiological forces in medical contexts.

Foundational Kinematics: Describing Motion

Kinematics is the study of motion without considering its causes. For the MCAT, you must be fluent in the translational motion equations (often called the "Big Five" or "SUVAT" equations) that relate displacement ($x$), initial velocity ($v_0$), final velocity ($v$), acceleration ($a$), and time ($t$). The core equations are:

$$v=v_0+at$$ $$x=v_{0}t+\frac{1}{2}a{t}^2$$ $$v^2=v_0^2+2ax$$

A crucial MCAT skill is selecting the correct equation by identifying which variables are given and which you need to find. For projectile motion, treat the horizontal and vertical components independently. Horizontal velocity remains constant (assuming no air resistance), while vertical motion experiences constant acceleration due to gravity ($g=9.8{\text{ m/s}}^2$, but estimate as $10{\text{ m/s}}^2$). The time of flight is determined exclusively by the vertical component. For example, a ball thrown horizontally from a table and another dropped from the same height will hit the ground simultaneously.

Dynamics: The Causes of Motion

Newton's laws form the cornerstone of dynamics. The First Law (inertia) states an object maintains its velocity unless acted upon by a net force. The Second Law ($F_{net}=ma$) quantifies this: net force causes proportional acceleration. The Third Law (action-reaction) notes forces come in equal-and-opposite pairs acting on different objects.

You will consistently apply $F_{net}=ma$ to systems. Key forces include:

• Gravity (Weight): $F_g=mg$, directed downward.
• Normal Force: The perpendicular contact force from a surface.
• Tension: The pulling force through a string, rope, or tendon.
• Friction: Kinetic friction ($f_k={\mu }_{k}N$) opposes sliding motion. Static friction ($f_s\le {\mu }_{s}N$) opposes the impending motion and adjusts up to a maximum.

Common scenarios are inclined planes and pulley systems. On an incline at angle $\theta$, resolve weight into components: $mg\sin \theta$ (parallel, down the ramp) and $mg\cos \theta$ (perpendicular, into the ramp). For a basic two-mass pulley system (Atwood machine), the net accelerating force is the difference in weights, and the total accelerated mass is the sum of both masses.

Work, Energy, and Conservation Laws

The work-energy theorem connects dynamics to energy: the net work done on an object equals its change in kinetic energy ($W_{net}=\Delta KE=\frac{1}{2}m{v}^2-\frac{1}{2}m{v}_0^2$). Work is done when a force causes displacement: $W=Fd\cos \theta$, where $\theta$ is the angle between the force and displacement vectors. Forces perpendicular to motion (like the normal force) do zero work.

Conservation of mechanical energy holds when only conservative forces (like gravity) act: $K{E}_i+P{E}_i=K{E}_f+P{E}_f$. For gravity, $P{E}_g=mgh$. Non-conservative forces like friction convert mechanical energy into thermal energy. The MCAT frequently tests energy transformations, such as a roller coaster's potential-to-kinetic energy conversion or a spring's potential energy ($P{E}_{spring}=\frac{1}{2}k{x}^2$).

Conservation of linear momentum ($p=mv$) is a separate, powerful law applied to isolated systems: $m_1{v}_{1i}+m_2{v}_{2i}=m_1{v}_{1f}+m_2{v}_{2f}$. It is essential for analyzing collisions. Perfectly inelastic collisions (objects stick together) maximize kinetic energy loss but conserve momentum. Elastic collisions conserve both momentum and kinetic energy.

Rotational Motion and Equilibrium

While translational motion follows linear analogs, rotational motion has its own parallel set of variables: angular displacement ($\theta$), angular velocity ($\omega$), and angular acceleration ($\alpha$). The corresponding kinematic equations are identical in form. The connection to linear motion is through the radius: $s=r\theta$, $v=r\omega$, $a_t=r\alpha$.

Torque ($\tau$) is the rotational equivalent of force and causes angular acceleration. $\tau =rF\sin \theta$, where $r$ is the lever arm distance from the pivot and $\theta$ is the angle between the force vector and lever arm. Maximize torque by applying force perpendicularly at the greatest distance from the pivot—a principle vital for understanding biomechanics like muscle action.

For an object to be in static equilibrium, two conditions must be met: (1) net force equals zero (translational equilibrium), and (2) net torque equals zero (rotational equilibrium). You will solve these problems by carefully selecting a pivot point to simplify torque calculations. The center of mass is the point where the weighted relative position of mass sums to zero; for a uniform object, it is at the geometric center.

Circular Motion and MCAT-Specific Strategies

Uniform circular motion involves constant speed but changing velocity (direction), meaning there is a centripetal acceleration directed toward the center. The magnitude is $a_c=\frac{v^2}{r}$. This acceleration is caused by a centripetal force, which is not a new force but the net result of others (e.g., tension, gravity, friction) pointing radially inward. A car turning on a flat road uses static friction as the centripetal force.

The MCAT prohibits calculators, so estimation strategies are non-negotiable.

• Round Numbers: Use $g\approx 10{\text{ m/s}}^2$, $\pi \approx 3$, $\sqrt{2}\approx 1.4$.
• Scientific Notation: Manage orders of magnitude separately. For $(3\times 10^4)\times (2\times 10^{-2})$, calculate $3\times 2=6$ and $10^4\times 10^{-2}=10^2$, giving $6\times 10^2$.
• Eliminate Implausible Answers: Often, dimensional analysis or a quick order-of-magnitude check removes two answer choices immediately.
• Focus on Proportionality: The MCAT loves to ask "If velocity doubles, what happens to kinetic energy?" ($KE\propto v^2$, so it quadruples).

Common Pitfalls

1. Confusing Velocity and Acceleration Directions in Circular Motion: Remember, velocity is tangential (along the path), while centripetal acceleration and force are radially inward. An object in circular motion is accelerating even at constant speed.
2. Misapplying Conservation Laws: Mechanical energy is not conserved if friction or air resistance acts. Momentum is not conserved if a significant external net force acts on the system (e.g., a person jumping from a cart provides an internal force, so cart-person system momentum is conserved).
3. Sign Errors with Gravity: Consistently define your positive direction. In kinematic equations, if down is positive, $g=+9.8{\text{ m/s}}^2$; if up is positive, $g=-9.8{\text{ m/s}}^2$. Mixing signs is a frequent source of error.
4. Overcomplicating Pulley Problems: For a single rope connecting objects over a massless, frictionless pulley, the tension is uniform throughout, and the magnitudes of acceleration for both objects are equal. Isolate each object with a free-body diagram and connect them via the tension and acceleration constraints.

Summary

• Kinematics describes motion via equations linking displacement, velocity, acceleration, and time. Projectile motion splits into independent horizontal (constant velocity) and vertical (constant acceleration) components.
• Dynamics explains motion through Newton's Laws. The core tool is $F_{net}=ma$, applied using free-body diagrams to analyze forces like gravity, normal force, tension, and friction in systems like inclines and pulleys.
• Work-Energy and Momentum provide powerful conservation approaches. The work-energy theorem links net work to kinetic energy change. Conserve mechanical energy (KE + PE) absent non-conservative forces, and always conserve momentum in isolated systems.
• Rotational Motion parallels linear motion with analogs like torque ($\tau =rF\sin \theta$) and angular kinematics. Static equilibrium requires both net force and net torque to be zero.
• MCAT Success hinges on conceptual integration, systematic problem-solving (identify, set up, execute), and mastering estimation techniques to bypass the lack of a calculator.