Mechanics Cheat Sheet: AS91171
Demonstrate a comprehensive understanding of mechanics by connecting concepts and applying mathematical solutions to described situations.
Core Principles
- Demonstrate understanding: Relate simple facets of phenomena, concepts, or principles to a situation.
- Demonstrate in-depth understanding: Explain reasons why phenomena, concepts, or principles relate to a situation, potentially using non-obvious mathematical solutions.
- Demonstrate comprehensive understanding: Show connections between different concepts within mechanics.
Action Steps
- 1. Identify all relevant motion concepts (Displacement, Velocity, Acceleration, Time).
- 2. Apply appropriate equations of motion to solve for unknowns.
- 3. Draw and interpret displacement-time and velocity-time graphs.
- 4. Analyze forces using diagrams, vector addition, and torque calculations.
- 5. Understand and apply conservation laws for momentum and energy.
- 6. Use correct significant figures and units in all calculations and statements.
- 7. Clearly explain the relationships between different mechanical concepts in your written statements.
Formulas
- Average Velocity: $v = \frac{\Delta d}{\Delta t}$
- Average Acceleration: $a = \frac{\Delta v}{\Delta t}$
- Velocity with Constant Acceleration: $v_{f} = v_{i} + at$
- Displacement with Constant Acceleration: $d = v_{i}t + \frac{1}{2} at^2$
- Displacement (average velocity): $d = \frac{v_{i} + v_{f}}{2} t$
- Velocity-Displacement Relation: $v_{f}^2 = v_{i}^2 + 2ad$
- Centripetal Acceleration: $a_{c} = \frac{v^2}{r}$
- Momentum: $p = mv$
- Impulse: $\Delta p = F\Delta t$
- Elastic Potential Energy: $E_{p} = \frac{1}{2} kx^2$
- Kinetic Energy: $E_{k} = \frac{1}{2}mv^2$
- Gravitational Potential Energy: $\Delta E_{p} = mg\Delta h$
- Work: $W = Fd$
- Power: $P = \frac{W}{t}$
- Newton's Second Law: $F = ma$
- Torque: $ au = Fd$
- Spring Force: $F = -kx$
- Centripetal Force: $F_{c} = \frac{mv^2}{r}$
Key Terms
- Displacement: The change in position of an object.
- Velocity: The rate of change of displacement; includes both speed and direction.
- Acceleration: The rate of change of velocity.
- Momentum: The product of an object's mass and its velocity (p = mv).
- Impulse: The change in momentum of an object, equal to the force applied multiplied by the time interval (Δp = FΔt).
- Conservation of Momentum: In a closed system, the total momentum remains constant.
- Conservation of Energy: In an isolated system, energy can be transformed from one form to another, but cannot be created or destroyed.
- Torque: A rotational force; the product of force and the perpendicular distance from the pivot point (τ = Fd).
- Equilibrium: A state where the net force and net torque on an object are zero, resulting in no change in motion.
- Spring Constant (k): A measure of the stiffness of a spring; relates the force exerted by the spring to its extension or compression (F = -kx).
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