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Contact Forces and Atwood Machine Dynamics Study Guide

This guide covers the essential principles of two-dimensional vector kinematics. It explains how to use Cartesian and Polar coordinate systems to describe motion, the different ways to represent vectors (magnitude-direction and unit vector notation), and the crucial concept of separating motion into independent x and y components. The guide also details the analysis of position and velocity vectors and the methods for performing vector addition, including the Law of Cosines.

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Kinematics and Newton's Laws of Motion

Linear Motion and Motion Graphs

An exploration of distance, displacement, velocity, acceleration, and jerk using position versus time and velocity versus time graphs.

  • distance
  • displacement
  • position versus time graph
  • velocity versus time graph
  • acceleration versus time graph
  • average speed
  • average velocity
  • instantaneous velocity
  • scalar quantity
  • vector quantity
  • particle
  • slope
  • jerk

Kinematic Equations and Free Fall Motion

An exploration of constant acceleration motion, free fall, and the relationship between position, velocity, and acceleration.

  • free fall
  • kinematic equations of motion
  • constant acceleration
  • initial velocity
  • final velocity
  • acceleration due to gravity
  • instantaneous velocity
  • average velocity
  • displacement

Kinematics of Particle Motion

Analysis of average velocity, instantaneous velocity, and acceleration for particles under constant velocity and constant acceleration models.

  • average velocity
  • instantaneous velocity
  • average speed
  • instantaneous speed
  • average acceleration
  • instantaneous acceleration
  • particle under constant velocity
  • particle under constant acceleration
  • displacement
  • position versus time
  • kinematic equations

Physics of Uniform Circular Motion

Analysis of forces, tangential velocity, and centripetal acceleration for objects moving in circular paths.

  • tangential velocity
  • centripetal force
  • centripetal acceleration
  • normal force
  • gravitational force
  • tension
  • air resistance
  • static friction
  • Newton's first law
  • second law
  • uniform circular motion
  • radial component
  • angular speed

Contact Forces and Atwood Machine Dynamics

Exploring laws through contact forces between blocks and the motion of an Atwood machine.

  • Newton's three laws
  • Contact forces
  • Free-body diagram
  • second law
  • Acceleration
  • Net force
  • Mass
  • External force
  • Kinematic equations
  • Displacement
  • Atwood machine
  • Tension
  • Inextensible cord
  • Gravitational force
  • Acceleration of gravity

Conceptual Understanding of Newton's Laws

Students discuss Newton's laws through a simulation of colliding trains to explore forces, mass, and acceleration.

  • Newton's first law
  • second law
  • Newton's third law
  • gravitational force
  • normal force
  • frictional force
  • mass
  • acceleration
  • velocity
  • net force

Newton's Second Law and Force Analysis

Analysis of particles in uniform circular motion, equilibrium, and constant acceleration using Newton's second law, tension, normal force, and friction.

  • second law
  • Centripetal acceleration
  • Normal force
  • Uniform circular motion
  • Particle in equilibrium
  • Kinetic friction
  • Fluid drag force
  • Terminal velocity
  • Tension
  • Free-body diagram
  • acceleration
  • friction force
  • coefficient of kinetic friction
  • equilibrium
  • net force model
  • particle in equilibrium model
  • gravitational force
  • mass
  • inclination

Two Dimensional Kinematics and Projectile Motion

Physics Chapter 1 Enhanced Assignment

A review of concepts in physical sciences and mathematics including density, volume, unit conversions, and geometric models.

  • density
  • volume
  • significant figures
  • unit conversions
  • right triangle
  • circumference
  • radius
  • sine
  • tangent
  • volume flow rate

Position and Time in Projectile Motion

A simulation explores how launch angle and initial speed affect the maximum height and horizontal range of a projectile in the absence of air resistance.

  • projectile motion
  • initial speed
  • launch angle
  • maximum height
  • maximum horizontal range
  • air resistance
  • kinematic equation
  • vertical direction
  • horizontal component of velocity
  • gravitational acceleration

Projectile Motion and Horizontal Range

Deriving the range equation for a projectile in the absence of air resistance on level ground using initial velocity and launch angle.

  • horizontal component of velocity
  • maximum height
  • range equation
  • projectile motion
  • launch angle
  • trigonometric identity
  • air resistance

Velocity Components in Projectile Motion

Analysis of the horizontal and vertical components of the velocity vector, launch angle effects, and gravitational acceleration in projectile motion.

  • horizontal component of velocity
  • vertical component of velocity
  • projectile motion
  • launch angle
  • gravitational acceleration
  • maximum height
  • range
  • time of flight
  • velocity vector
  • complementary angles
  • kinematic equations

Motion Under Constant Acceleration

Analysis of a particle's motion using initial position, initial velocity, and constant acceleration components.

  • constant acceleration
  • velocity vector
  • position vector
  • acceleration components
  • initial conditions
  • direction of acceleration
  • final velocity

Projectile Motion and Kinematic Analysis

Analysis of projectile motion using particle under constant velocity and particle under constant acceleration models to determine velocity components, trajectory, and time.

  • projectile
  • air resistance
  • horizontal component of motion
  • vertical component of motion
  • acceleration due to gravity
  • particle under constant velocity
  • particle under constant acceleration
  • velocity components
  • trajectory
  • initial velocity
  • launch angle

Cartesian and Polar Coordinates

Understanding the relationship between Cartesian and polar coordinates through trigonometry and coordinate system conversions.

  • Cartesian coordinates
  • Polar coordinates
  • Trigonometric functions
  • Sine
  • Tangent
  • Quadrant signs
  • Radial motion
  • Force components

Two Dimensional Vector Kinematics and Notation

The sources cover the use of components, magnitude, direction, and unit vector notation to analyze displacement, velocity, and position in two dimensions.

  • magnitude and direction notation
  • two dimensional vector addition
  • unit vector notation
  • separation of motion into components
  • Cartesian coordinates
  • polar coordinates
  • particle under constant velocity model
  • law of cosines
  • position vector
  • velocity vector

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