Physics Semester 1 Exam Review: Study Notes on Kinematics, Forces, and Circular Motion

1D Kinematics

Representing Motion and Position-Time Graphs

Understanding motion in one dimension involves analyzing position, velocity, and acceleration as functions of time. Graphical representations help visualize how these quantities change.

• Position-Time Graph (x vs t): Shows how an object's position changes over time. The slope at any point gives the velocity.

• Velocity-Time Graph (v vs t): Shows how velocity changes over time. The slope gives acceleration; the area under the curve gives displacement.

• Acceleration-Time Graph (a vs t): Shows how acceleration changes over time.

• Example: A student starts at rest, walks forward, stops, then walks backward. The position-time graph would show a positive slope (forward motion), a flat segment (stopped), and a negative slope (backward motion).

Free Fall and Acceleration Due to Gravity

Objects in free fall experience constant acceleration due to gravity, typically $g = 9.8\ \text{m/s}^2$ downward.

• Key Equations:

  • $v = v_0 + at$

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

  • $v^2 = v_0^2 + 2a(x - x_0)$

• Example: A ball is tossed straight down with an initial velocity; its velocity increases due to gravity.

Interpreting Graphs and Calculating Velocity

Velocity can be determined from position-time graphs by calculating the slope between two points.

• Average Velocity: $v_{avg} = \frac{\Delta x}{\Delta t}$

• Instantaneous Velocity: Slope of the tangent to the curve at a specific time.

• Example: Using a position-time graph, calculate velocity between $t = 0$ and $t = 2$ s.

2D Kinematics

Projectile Motion

Projectile motion involves two-dimensional movement under gravity, with horizontal and vertical components analyzed separately.

• Horizontal Motion: Constant velocity, $x = v_{0x} t$

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

• Maximum Height: $h_{max} = \frac{v_{0y}^2}{2g}$

• Range: $R = \frac{v_0^2 \sin 2\theta}{g}$

• Example: An object is thrown at an angle; calculate time to reach maximum height and total time of flight.

Relative Motion and Vector Components

Motion in two dimensions requires resolving vectors into components and using vector addition.

• Component Formulas:

  • $v_x = v \cos \theta$

  • $v_y = v \sin \theta$

• Example: Calculate the x- and y-components of velocity for a car falling off a cliff.

Forces & Newton's Laws

Free-Body Diagrams (FBDs)

Free-body diagrams are essential for visualizing all forces acting on an object.

• Steps to Draw FBD:

  1. Represent the object as a dot or box.

  2. Draw arrows for all forces (gravity, normal, friction, applied, tension).

  3. Label each force clearly.

• Example: Draw an FBD for a box on a rough surface with an applied force.

Static and Kinetic Friction

Friction opposes motion between surfaces. Static friction prevents motion; kinetic friction acts during motion.

• Static Friction: $f_s \leq \mu_s N$

• Kinetic Friction: $f_k = \mu_k N$

• Normal Force: Perpendicular contact force from a surface.

• Example: Calculate the maximum static friction for a box with given mass and coefficient.

Newton's Second Law

Newton's Second Law relates net force to acceleration: $F_{net} = ma$.

• Application: Sum all forces in the direction of motion to find acceleration.

• Example: A box is pushed with a force; calculate acceleration considering friction.

Uniform Circular Motion

Angular Speed vs Tangential Speed

Objects moving in circles have both angular and tangential speeds.

• Angular Speed ($\omega$): Rate of change of angle, $\omega = \frac{\theta}{t}$ (radians per second).

• Tangential Speed ($v$): Linear speed along the circular path, $v = r \omega$.

• Example: Compare angular and tangential speeds for a person sitting at different radii on a carousel.

Centripetal Force and Acceleration

Circular motion requires a net inward force (centripetal force) to maintain the path.

• Centripetal Acceleration: $a_c = \frac{v^2}{r}$

• Centripetal Force: $F_c = m a_c = m \frac{v^2}{r}$

• Example: Calculate the tension in a string for a ball moving in a vertical circle.

Free-Body Diagrams in Circular Motion

For objects in circular motion, FBDs help identify forces such as tension, gravity, and normal force.

• Example: Draw an FBD for a ball at the top of a vertical circle.

Summary Table: Key Equations

Topic	Equation	Description
1D Kinematics	$v = v_0 + at$	Velocity with constant acceleration
1D Kinematics	$x = x_0 + v_0 t + \frac{1}{2} a t^2$	Position with constant acceleration
2D Kinematics	$R = \frac{v_0^2 \sin 2\theta}{g}$	Projectile range
Forces	$F_{net} = ma$	Newton's Second Law
Friction	$f_s \leq \mu_s N$	Static friction
Friction	$f_k = \mu_k N$	Kinetic friction
Circular Motion	$a_c = \frac{v^2}{r}$	Centripetal acceleration
Circular Motion	$F_c = m \frac{v^2}{r}$	Centripetal force

Additional info: These notes expand on the exam review questions by providing definitions, formulas, and examples for each major topic covered in the provided materials.