Representing Motion

Position, Displacement, and Graphical Analysis

Understanding motion begins with representing the position of objects and analyzing their displacement over time. Graphs and tables are essential tools for visualizing and interpreting motion.

• Position: The location of an object at a particular time, often denoted as x or y.

• Displacement: The change in position, calculated as .

• Graphical Analysis: Position vs. time and velocity vs. time graphs help determine speed, acceleration, and other motion characteristics.

• Example: A graph showing the relationship between body size and claw size in a crab, with a linear fit indicating proportional growth.

Motion in One Dimension

Kinematics and Velocity-Time Graphs

One-dimensional motion involves objects moving along a straight line, described by position, velocity, and acceleration.

• Velocity: The rate of change of position, .

• Acceleration: The rate of change of velocity, .

• Equations of Motion: For constant acceleration:

• Example: Calculating the distance a cyclist travels using the area under a velocity-time graph.

Vectors and Motion in Two Dimensions

Projectile Motion and Relative Velocity

Two-dimensional motion includes projectile motion and the analysis of objects moving in a plane.

• Projectile Motion: The motion of an object thrown into the air, subject only to gravity.

  • Horizontal motion:

  • Vertical motion:

• Relative Velocity: The velocity of an object as observed from a particular reference frame.

• Example: Calculating the range and time of flight for a soccer ball kicked at an angle.

Forces & Newton's Laws of Motion

Fundamental Laws and Applications

Newton's laws describe the relationship between forces and motion.

• Newton's First Law: An object remains at rest or in uniform motion unless acted upon by a net force.

• Newton's Second Law:

• Newton's Third Law: For every action, there is an equal and opposite reaction.

• Example: Calculating the net force required to stop a moving car.

Applying Newton's Laws

Friction, Inclined Planes, and Tension

Newton's laws are applied to analyze forces in various scenarios, including friction and tension.

• Friction: The resistive force between surfaces, .

• Inclined Planes: Forces are resolved into components parallel and perpendicular to the surface.

• Tension: The force transmitted through a string, rope, or cable.

• Example: Two blocks colliding on a frictionless ramp and analyzing their velocities post-collision.

Circular Motion, Orbits & Gravity

Uniform Circular Motion and Centripetal Force

Objects moving in circles experience centripetal acceleration and force.

• Centripetal Acceleration:

• Centripetal Force:

• Example: Calculating the maximum speed of a ball on a string before it breaks.

Rotational Motion

Angular Velocity and Acceleration

Rotational motion involves objects spinning about an axis.

• Angular Velocity:

• Angular Acceleration:

• Example: Calculating the angular acceleration of a wheel.

Equilibrium & Elasticity

Static Equilibrium and Springs

Equilibrium occurs when the net force and net torque on an object are zero.

• Spring Force:

• Elastic Potential Energy:

• Example: Determining the compression of a spring when a block is placed on it.

Momentum

Conservation of Momentum and Impulse

Momentum is conserved in isolated systems, and impulse relates to the change in momentum.

• Momentum:

• Impulse:

• Conservation of Momentum:

• Example: Calculating the impulse delivered to a ball during a collision.

Energy & Work

Kinetic, Potential Energy, and Work

Energy can be transferred or transformed, and work is the process of energy transfer.

• Kinetic Energy:

• Potential Energy:

• Work:

• Work-Energy Theorem:

• Example: Calculating the work done by a force pulling a crate across a rough floor.

Using Energy

Conservation of Energy and Power

The total energy in a closed system remains constant.

• Conservation of Energy:

• Power:

• Example: Analyzing energy changes in a block-spring system.

Additional Info: Tables and Data Interpretation

Using Tables and Graphs in Physics Problems

Tables and graphs are frequently used to present experimental data and relationships between variables.

This table shows a linear relationship between body size and claw size, which can be analyzed using regression or graphical methods.

Summary Table: Key Equations

Additional info: These notes cover the main topics and equations relevant to the Physics 114 final exam, including motion, forces, energy, and momentum, as indicated by the exam questions and diagrams.