Exam 1 Physics Study Guide: Kinematics, Vectors, and Forces

Exam 1 Coverage: Physics Fundamentals

Chapter 2: Kinematics in One Dimension

Kinematics is the study of motion without considering its causes. This chapter introduces the foundational concepts of position, displacement, speed, velocity, and acceleration, and how to mathematically describe motion in one dimension.

• Position, Displacement, and Total Distance Traveled: Position refers to the location of an object. Displacement is the change in position, a vector quantity. Total distance is the scalar sum of all movement.

• Velocity vs Speed: Speed is a scalar (magnitude only), while velocity is a vector (magnitude and direction).

• Acceleration: The rate of change of velocity. $a = \frac{dv}{dt}$

• Average vs Instantaneous: Average velocity is total displacement divided by total time. Instantaneous velocity is the velocity at a specific moment.

• Applying Kinematic Equations to Describe 1D Motion: The following equations are used for constant acceleration:

  • $v = v_0 + at$

  • $x = x_0 + v_0 t + \frac{1}{2} a t^2$

  • $v^2 = v_0^2 + 2a(x - x_0)$

• Graphical Representation of Kinematics: Position-time, velocity-time, and acceleration-time graphs help visualize motion.

• Free Fall: Objects in free fall experience constant acceleration due to gravity. $g = -9.8\ \text{m/s}^2$

Chapter 3: Vectors and Two-Dimensional Motion

This chapter extends kinematics to two dimensions, introducing vectors and their operations, and applying kinematic equations to projectile motion.

• Displacement, Velocity, and Acceleration as Vectors:

  • Trig Functions: Used to resolve vectors into components.

  • Adding Vectors: Vectors are added using the head-to-tail method or by components.

  • Unit-Vector Notation: Expresses vectors in terms of $\hat{i}$, $\hat{j}$, and $\hat{k}$.

• Applying Kinematic Equations to Describe 2D Motion: Each direction (x and y) is treated independently using kinematic equations.

• Projectile Motion:

  • Maximum Height: The highest point reached by a projectile.

  • Range: The horizontal distance traveled.

  • Time of Flight: The total time the projectile is in the air.

  Key Equations:

  • Horizontal: $x = v_{0x} t$

  • Vertical: $y = v_{0y} t - \frac{1}{2} g t^2$

Chapters 4 & 5: Forces and Newton's Laws

These chapters introduce the concept of force, Newton's laws of motion, and various types of forces encountered in physics.

• Concept of Force: A force is a push or pull that can change an object's motion.

• Force as a Vector: Forces have both magnitude and direction.

• Newton's Law of Motion:

  • Net Force: The vector sum of all forces acting on an object.

  • Inertia: The tendency of an object to resist changes in its motion. Constant velocity means net force is zero (no acceleration).

  Newton's Second Law:

  • $\vec{F}_{\text{net}} = m \vec{a}$

• Types of Forces:

  • Reaction Force: Includes tension and normal force.

  • Restoring Force: Includes gravity and spring force.

  • Weight vs Mass: Mass is the amount of matter; weight is the force due to gravity. $W = mg$

  • Drag (Conceptual Only):

    • Factors that influence drag include shape, speed, and fluid properties.

    • Air resistance is a common example of drag.

  • Friction Force:

    • Kinetic vs Static Friction: Static friction acts when objects are at rest; kinetic friction acts when objects are moving.

    • Proportional to Normal Force: Frictional force depends on the normal force.

    • Coefficient of Friction ($\mu$): $f = \mu N$

  • Elasticity Concept Only: Elasticity describes how materials return to their original shape after deformation.

Topics Not Included on Exam 1

• Atwood Machine (from Chapters 4/5)

• Elastic Modulus Equation (from Chapter 5)

• Shear Modulus Equation (from Chapter 5)