Overview
This lecture covers essential mechanical comprehension topics for Army Aviation test prep, focusing on motion, forces, energy, and related concepts.
Motion: Distance, Displacement, and Graphs
- Distance is a scalar measuring the total length traveled; displacement is a vector measuring straight-line change in position.
- Scalar quantities have only magnitude; vector quantities have magnitude and direction.
- Distance-time graphs show rest, acceleration, constant speed, and return journeys.
- Velocity is displacement over time and is a vector; common units are m/s or ft/s.
- Velocity-time graphs illustrate constant velocity, acceleration, and irregular motions.
- Acceleration is the rate of change of velocity over time; zero acceleration means constant speed.
- In velocity-time graphs, acceleration equals the slope; displacement equals the area under the curve.
Two-Dimensional & Circular Motion
- Projectile motion involves objects moving in two dimensions under gravity.
- Maximum velocity is at the start; velocity is zero at the topmost point and when the object lands.
- Air resistance alters both vertical and horizontal velocity profiles.
- Circular motion describes movement along a circular path; linear velocity v = ωr (where ω is angular velocity and r is radius).
- When an object is released from circular motion, it moves tangentially.
Forces & Types of Forces
- Force (F) equals mass (m) times acceleration (a): F = ma (Newton’s Second Law).
- Types of forces include weight (gravity), friction, air resistance, tension, and normal force.
- Friction resists motion between surfaces and appears as rolling or static friction.
- Rolling friction slows moving objects (e.g., a bicycle coasting); static friction must be overcome to start movement.
Springs, Stress & Strain
- Spring force follows Hooke’s Law: F = -kx, where k is the spring constant and x is displacement.
- For series springs: 1/keq = 1/k1 + 1/k2; for parallel springs: keq = k1 + k2.
- Stress is force per unit area on a material; strain is change in length divided by original length.
- Types of stress: compression (pushing), tension (pulling), shear (sliding), bending, and torsion (twisting).
Torque, Work, Energy & Power
- Torque (τ) is force multiplied by distance from the pivot; causes rotational motion.
- Work equals force times displacement; work is done only if the object moves.
- Less work is required to move an object at an angle than horizontally.
- Energy is the ability to do work; forms include mechanical, kinetic, potential, heat, sound, electric, chemical, and nuclear.
- Power is work done per unit time; efficiency is output power/input power as a ratio.
Pendulums
- The pendulum bob's speed is greatest at the equilibrium (lowest) position and zero at the maximum height.
Key Terms & Definitions
- Scalar — quantity with only magnitude (e.g., distance).
- Vector — quantity with magnitude and direction (e.g., displacement, velocity).
- Acceleration — rate of change of velocity over time.
- Friction — force resisting motion between surfaces.
- Hooke’s Law — relationship for spring force: F = -kx.
- Stress — force per unit area on a material.
- Strain — ratio of deformation to original length.
- Torque (τ) — rotational force: τ = force × distance from pivot.
- Work — force applied over a distance.
- Power — rate of doing work.
Action Items / Next Steps
- Practice drawing and interpreting motion graphs.
- Memorize key formulas (F = ma, F = -kx, v = ωr, work = force × distance).
- Review types of stress and be able to identify them in diagrams.
- Download the SIP Tutoring App and practice relevant sections.