BackPHYS407 Exam 3 Study Guide: Dynamics, Conservation Laws, and Problem Solving
Study Guide - Smart Notes
Tailored notes based on your materials, expanded with key definitions, examples, and context.
Chapter 8: 2D Dynamics
Uniform Circular Motion
Motion in a plane often involves circular trajectories. In uniform circular motion, a particle moves at constant speed along a circular path. The acceleration is always directed toward the center of the circle (centripetal acceleration).
Centripetal Acceleration: The magnitude is given by: where v is the tangential velocity and r is the radius of the circle.
Uniform Circular Motion: The speed is constant, but the direction of velocity changes continuously, resulting in acceleration toward the center.
Example: A car turning in a circle, or a planet orbiting the Sun.
Conservation Laws
System Definition
To apply conservation laws, clearly define the system. The system must include all objects whose energy or momentum you wish to track. For example, if a block slides down a ramp, the system could be just the block, or the block plus the Earth.
Isolated System: No energy or momentum enters or leaves the system.
Example: Block sliding down a frictionless ramp (block + Earth as system).
Momentum and Impulse
Momentum is a measure of an object's motion, defined as the product of mass and velocity. Impulse is the change in momentum resulting from a force applied over time.
Momentum:
Impulse:
Newton's Second Law (Integral Form):
Example: A bat hitting a baseball applies an impulse, changing the ball's momentum.
Work
Work is the transfer of energy by a force acting over a distance. It is defined as the integral of force along the path of motion.
Work (General Definition):
Work (Constant Force, Straight Path):
Example: Lifting a box vertically:
Conservation of Energy
The total energy of an isolated system remains constant. Energy can be transformed between kinetic and potential forms, but the sum is conserved.
Conservation of Energy Equation: or where is kinetic energy and is potential energy.
Example: A pendulum swings: potential energy converts to kinetic and back, but total energy remains constant.
Collisions
Collisions are classified as elastic or inelastic. In elastic collisions, both momentum and kinetic energy are conserved. In inelastic collisions, momentum is conserved but kinetic energy is not.
Type | Momentum Conserved? | Kinetic Energy Conserved? |
|---|---|---|
Elastic | Yes | Yes |
Inelastic | Yes | No |
Example: Billiard balls colliding (elastic); car crash (inelastic).
Power
Power is the rate at which work is done or energy is transferred.
Power Formula:
Example: Lifting a weight at constant speed requires constant power.
Steps for Solving Problems
Physics problems often require a systematic approach. Follow these steps:
Identify the system and draw a free-body diagram.
Use Newton's laws to relate forces to acceleration and motion.
If conservation laws apply, write the relevant equations for energy or momentum.
Solve for the unknowns using algebraic manipulation.
Check units and physical plausibility of your answer.
Additional info: These notes cover topics from chapters 8-11 in Knight, including 2D dynamics, conservation laws, work, energy, collisions, and power, which are all central to a college-level physics course.
