CH 3 | Two-Dimensional Kinematics

Two-Dimensional Kinematics

Motion along a curved path on a flat surface or a plane

Three-Dimensional Kinematics

Motion not confined to a plane, such as a car following a winding mountain road

Straight-Line Path Equation

If two legs of a trip form a right triangle, then the Pythagorean theorem can be used: a^2+b^2=c^2

Straight-Line Distance

Less than the total distance of the entire trip

Vectors Not Perpendicular

The Pythagorean theorem cannot be used to calculate the magnitude of total displacement

Independence of Motion

Any motion in the horizontal direction does not affect motion in the vertical direction, and vice versa

Projectile Motion

The motion of an object thrown or projected into the air, subject to only the acceleration of gravity

Vectors in Two Dimensions

Specify the direction of the vector relative to some reference frame, using an arrow having length proportional to the vector’s magnitude

Drawing Vectors

Draw a line from the tail of the first vector to the head of the second vector to form the sum of the resultant vector

True

Vectors can be added in any order

Multiplying by a Positive Scalar

The magnitude changes but direction stays the same

Multiplying by a Negative Scalar

Changes the vector’s magnitude and gives the new vector the opposite direction

Components of a Vector

The x- and y- or the north-south and east-west parts

Analytical Methods

The method of determining the magnitude and direction of a resultant vector using the Pythagorean theorem and trigonometric identities

Degree of Vector

tan^-1(y/x)

Perpendicular Components

x=Acos(𝛳) and y=Asin(𝛳)

Vector Subtraction

The addition of a negative vector

Trajectory

Path of a projectile

Projectile

An object that travels through the air and experiences only acceleration due to gravity

True

Vertical and horizontal motions are independent

Apex

Highest point in any trajectory that is reached when vy=0

Range

The maximum horizontal distance traveled by a projectile

Orbit

The Earth curves away from underneath the object at the same rate as it falls

Relativity

The study of how different observers moving relative to each other measure the same phenomenon

Classical Relativity

The study of relative velocities limited to situations where speeds are less than 1% the speed of light, so less than 3000 km/s

Air Resistance

A frictional force that slows the motion of objects as they travel through the air; when solving basic physics problems, it is assumed to be zero

Commutative

Refers to the interchangeability of order in a function; vector addition is commutative because the order in which vectors are added together does not affect final sum

Direction (Of a Vector)

Orientation of a vector in space

Kinematics

Study of motion without regard to mass or force

Resultant

Sum of two or more vectors

Direction of an Angle

X degrees [moving toward] of [reference baseline]