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Rotation, Torque & Equilibrium
Forces make objects accelerate; torques make them spin. You will compute torques, solve beam and lever equilibrium problems, use rotational kinematics and angular momentum, and analyze simple machines and pulleys with clean numbers.
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What this chapter covers
- Torque and the Lever Arm. Torque is the rotational version of force, and the MCAT loves testing where and at what angle the force is applied.
- Static Equilibrium of Beams and Levers. Beam, plank, and see-saw problems are the classic MCAT torque question. Pick a smart pivot and the algebra collapses.
- Rotational Kinematics. Rotational motion mirrors linear motion. Learn the analogies and the link v = rω, and half the topic is already done.
- Rotational Dynamics & Angular Momentum. Moment of inertia is rotational mass, and conservation of angular momentum explains skaters, divers, and many MCAT thought experiments.
- Simple Machines & Pulleys. Machines trade force for distance but never for work. Counting rope segments and comparing lever arms solves nearly every MCAT machine question.
Key points to know
- τ = r F sin θ; lever arm = perpendicular distance from pivot to force line
- Torque is maximum when F is perpendicular to r (θ = 90°)
- Static equilibrium: ΣF = 0 and Στ = 0
- Pick a pivot at an unknown force to eliminate it
- ω = Δθ/Δt (rad/s); α = Δω/Δt (rad/s²); ω = 2πf
- Rotational kinematics equations mirror the linear ones
- τ_net = Iα; I = Σmr² grows with mass distance squared
- L = Iω is conserved when net external torque is zero
Try a practice question
A force acts on a wrench along a line that passes directly through the center of the bolt (the pivot). What is the torque of this force about the bolt?
- Maximum, because the force is applied to the wrench
- Equal to the force times the wrench length
- Zero, because the lever arm is zero
- Negative, because the force points inward
Show the answer
C. The lever arm is the perpendicular distance from the pivot to the line of the force. A line through the pivot has zero lever arm, so the torque is zero regardless of the force size.
Common questions
What does this chapter cover?
Rotation, Torque & Equilibrium covers Torque and the Lever Arm, Static Equilibrium of Beams and Levers, Rotational Kinematics, Rotational Dynamics & Angular Momentum, Simple Machines & Pulleys.
What should I know first?
τ = r F sin θ; lever arm = perpendicular distance from pivot to force line Torque is maximum when F is perpendicular to r (θ = 90°) Static equilibrium: ΣF = 0 and Στ = 0
24 original practice questions accompany this chapter in the app. Spaced review brings missed ideas back at the right time; it helps memory but cannot promise you will not miss an idea again.