Physics Exam 2 Study Guide: Mechanics, Energy, and Momentum

Exam 2 Study Guide: Mechanics, Energy, and Momentum

Overview

This study guide covers essential topics in introductory college physics, focusing on mechanics, energy, and momentum. It includes definitions, formulas, and explanations relevant to exam questions, as well as examples and applications.

Key Formulas and Definitions

Time and Motion

• Time (t): Duration over which an event occurs.

• Velocity (v): Rate of change of position; $v = \frac{d}{t}$

• Acceleration (a): Rate of change of velocity; $a = \frac{v_f - v_i}{t}$

Linear Momentum and Impulse

• Linear Momentum (p): Product of mass and velocity; $p = m v$

• Impulse (J): Change in momentum; $J = F \Delta t$ or $J = \Delta p$

• Net Linear Momentum: Sum of all momenta in a system.

• Impulse-Momentum Theorem: $J = \Delta p$

• Newton's Second Law (Impulse Form): $F = \frac{dp}{dt}$

Work and Energy

• Work (W): Product of force and displacement in the direction of force; $W = F d \cos(\theta)$

• Kinetic Energy (KE): Energy due to motion; $KE = \frac{1}{2} m v^2$

• Potential Energy (PE): Energy due to position; Gravitational Potential Energy: $GPE = mgh$

• Total Mechanical Energy: $E_{total} = KE + PE$

• Work-Energy Theorem: $\Delta KE = W_{net}$

• Efficiency: $\text{Efficiency} = \frac{\text{Useful energy output}}{\text{Total energy input}}$

Conservation Laws

• Conservation of Linear Momentum: In a closed system, total linear momentum remains constant unless acted upon by external forces.

• Conservation of Energy: Total energy in a closed system remains constant; energy can be transformed but not created or destroyed.

• Conservation of Angular Momentum: Total angular momentum remains constant in the absence of external torques.

Collisions

• Elastic Collision: Both momentum and kinetic energy are conserved.

• Inelastic Collision: Momentum is conserved, but kinetic energy is not; objects may stick together.

Rotational Motion

• Torque (\tau): Rotational equivalent of force; $\tau = r F$

• Moment of Inertia (I): Resistance to rotational acceleration; $I = \sum m r^2$

• Angular Velocity (\omega): Rate of change of angular position.

• Angular Momentum (L): $L = I \omega$

Topic Explanations and Examples

Linear Momentum and Impulse

Linear momentum is a measure of an object's motion, dependent on mass and velocity. Impulse is the effect of a force applied over a time interval, resulting in a change in momentum.

• Key Point: Impulse equals the change in momentum ($J = \Delta p$).

• Example: A baseball hit by a bat experiences an impulse, changing its velocity.

Work and Power

Work is done when a force causes displacement. Power is the rate at which work is done.

• Key Point: $W = F d \cos(\theta)$; Power $P = \frac{W}{t}$

• Example: Lifting a box vertically requires work against gravity.

Mechanical Energy

Mechanical energy is the sum of kinetic and potential energies in a system.

• Key Point: $E_{total} = KE + PE$

• Example: A pendulum at its highest point has maximum potential energy; at its lowest, maximum kinetic energy.

Conservation of Energy and Momentum

Conservation laws are fundamental in physics, stating that certain quantities remain constant in isolated systems.

• Key Point: Energy and momentum are conserved in closed systems.

• Example: In a collision, total momentum before and after is the same.

Collisions: Elastic vs. Inelastic

Collisions are classified based on energy conservation.

• Elastic: Both momentum and kinetic energy conserved.

• Inelastic: Only momentum conserved; kinetic energy lost.

• Example: Bouncing balls (elastic); car crash with crumpling (inelastic).

Rotational Motion and Torque

Rotational motion involves objects spinning around an axis. Torque causes rotational acceleration.

• Key Point: $\tau = r F$; $I = \sum m r^2$

• Example: Opening a door applies torque at a distance from the hinge.

Angular Momentum and Its Conservation

Angular momentum is conserved in the absence of external torques.

• Key Point: $L = I \omega$

• Example: A spinning ice skater pulls in arms to spin faster (conservation of angular momentum).

Universal Law of Gravity

Newton's law describes the gravitational force between two masses.

• Key Point: $F = G \frac{m_1 m_2}{r^2}$

• Example: The force between Earth and the Moon.

Equilibrium and Stability

Equilibrium occurs when all forces and torques are balanced.

• Key Point: For static equilibrium, $\sum F = 0$ and $\sum \tau = 0$

• Example: A seesaw balanced at its center.

Summary Table: Mechanical Quantities

Quantity	Definition	Formula	Units
Linear Momentum	Mass times velocity	$p = m v$	kg·m/s
Impulse	Change in momentum	$J = F \Delta t$	N·s
Kinetic Energy	Energy of motion	$KE = \frac{1}{2} m v^2$	Joule (J)
Potential Energy	Energy due to position	$PE = mgh$	Joule (J)
Torque	Rotational force	$\tau = r F$	N·m
Angular Momentum	Rotational analog of momentum	$L = I \omega$	kg·m2/s

Additional info:

• Some formulas and definitions have been expanded for clarity and completeness.

• Examples and applications are provided to illustrate key concepts.

• Topics are grouped logically based on exam question list and formula sheet.