Midterm 1 Content Guide: Physics 5A

Overview

This guide outlines the topics covered on the first midterm for Physics 5A at UCLA. The exam focuses on foundational concepts in vectors, kinematics, and introductory circular motion, as presented in the course textbook and lectures. Students should use this guide to direct their study and practice efforts.

Topics Covered

Vectors and Vector Math

Vectors are quantities that have both magnitude and direction, essential for describing physical phenomena in physics. Understanding vector operations is crucial for solving problems in kinematics and dynamics.

• Definition of a Vector: A quantity with both magnitude and direction (e.g., displacement, velocity, acceleration).

• Vector Addition and Subtraction: Combine vectors using the head-to-tail method or by components.

• Components of Vectors: Any vector can be broken into x and y components using trigonometry.

• Vector Notation: Vectors are often denoted with arrows or boldface (e.g., v).

• Vector Math (Section 4.7): Includes operations such as dot product and cross product.

Example: The displacement vector from point A to point B can be written as , where and are the components along the x and y axes.

Kinematics: Basics of Motion

Kinematics is the study of motion without considering its causes. It involves describing the position, velocity, and acceleration of objects.

• Position: The location of an object in space, often described by coordinates.

• Displacement: The change in position of an object, a vector quantity.

• Velocity: The rate of change of displacement; a vector quantity.

• Acceleration: The rate of change of velocity; a vector quantity.

• Constant Acceleration: Motion where acceleration remains constant over time.

Key Equations:

Example: An object dropped from rest experiences constant acceleration due to gravity ().

Free-Fall Motion

Free-fall describes the motion of objects under the influence of gravity alone, neglecting air resistance.

• Acceleration Due to Gravity: downward near Earth's surface.

• Equations of Motion: Same as constant acceleration, with .

Example: A ball dropped from a height will reach the ground in time .

Projectile Motion

Projectile motion involves objects launched into the air, moving under the influence of gravity. The motion can be analyzed in horizontal and vertical components.

• Horizontal Motion: Constant velocity ().

• Vertical Motion: Constant acceleration ().

• Trajectory: The path is a parabola.

Key Equations:

• Horizontal displacement:

• Vertical displacement:

Example: A ball thrown at an angle with initial speed has initial components , .

Circular Motion Kinematics

Circular motion refers to the movement of an object along a circular path. Kinematics of circular motion involves angular quantities and their relationships.

• Angular Displacement (): The angle swept by the radius vector.

• Angular Velocity (): Rate of change of angular displacement.

• Angular Acceleration (): Rate of change of angular velocity.

• Relationship to Linear Quantities: ,

Example: An object moving in a circle of radius at constant speed has a centripetal acceleration directed toward the center.

Textbook Sections for Reference

• Chapter 2: Basics of motion and kinematics

• Chapter 3, Sections 3.1-3.7: Velocity, acceleration, constant acceleration motion, free-fall motion, projectile motion

• Section 4.7: Vector math

• Section 7.1: Circular motion kinematics

Practice Tests Guidance

• Practice tests are aligned with midterm content.

• Practice Test A includes circular motion; consider taking it after covering that topic.

• Practice Test C contains a Newton's 2nd law question; skip that part if not yet covered.

• Simulate exam conditions when taking practice tests for best preparation.

Additional info: The guide does not include material from Chapter 4 on forces and Newton's laws, except for vector math. Students should focus on the listed topics for Midterm 1 preparation.