Ch.2 Vectors
A Vector in Polar Coordinates
1) The magnitude of A is Ar. 2) theta is the angle measured Between A and the x-axis.
Different ways to write vectors
1. Cartesian 2. Polar
Motion can be obtained from position-versus-time graphs as follows:
1. Determine an object's position at a time t by reading a graph at that instant. 2. Determine the object's velocity at time t by finding the slope of the position graph at that point. Steeper slopes correspond to faster speeds. 3. Determine the direction of motion by noting the sign of the slope. Positive slopes correspond to positive velocities and, hence, to motion to the right (or up). Negative slopes correspond to negative velocities and, hence, to motion to the left (or down) .
Describing motion in one dimension
1. For all motion: Velocity is the rate of change of position, in m/s Acceleration is the rate of change of velocity, in m/s^2 2. For uniform motion: Acceleration is zero Velocity is constant position changes steadily 3. For motion with constant acceleration: The acceleration is constant, so the slope of the velocity graph is constant. Velocity changes steadily Final and initial Velocity (m/s) (Vx)f = (Vx)i + Ax*delta T The position changes as the square of the time interval The velocity steadily increases, so the slope of the position graph steadily increases. Xf = Xi + (Vx)i*deltaT + 1/2Ax(deltaT)^2 We can also express the change in velocity in terms of distance, not time. (Vx)f^2 = (Vx)i^2 +2Ax (deltaT)
Instantaneous Velocity
An object's velocity a speed and a direction at a specific instant of time t. The slope of the tangent line is the instantaneous velocity at that instance of time.
If the initial velocity is zero and the initial X displacement is zero:
Constant acceleration reduces to: Xf=1/2Ax(deltaT)^2
Free fall acceleration always points
Down!! No matter what direction the object is moving. Some examples: Note: Any object moving under the influence of gravity ONLY, is free falling. Throwing a football Objects that have been tossed Objects that have shot straight up A satellite in orbit
Free Fall
If an object moves under the influence of gravity only, and no other forces, we call the resulting motion free fall.
Uniform Motion
Straight-line motion in which equal displacements occur during ANY(constant) successive equal-time intervals.
Kinematics
The name of the mathematical description of motion.
Slopes of a graph
This ratio has a physical meaning it's the velocity! The slope of an object's position-versus-time-graph- is the objects velocity at that point in the motion.
Example 2.25 Analyzing the motion of a ball tossed upward
Turning point: The highest point in the ball's motion, where it reverses direction, is called the TURNING POINT.
Multiplying Vectors-Two methods
Two methods: Dot product-results in scalar Cross product-results in a vector
The magnitude of the free fall acceleration has the special symbol g:
g = 9.80 m/s^2 Note: There will Never be a problem that uses g = -9.80 m/s^2 Acceleration on the other hand can be either negative or positive. This indicated the direction and speed of the object. Ay= -g, where g is not gravity but the FREE FALL ACCELERATION.
Speed
is the magnitude of the velocity vector and is ALWAYS POSITIVE.
Determining the sign of the acceleration
need to copy notes on onenote over from pc.
Ex. 2.1
note: try to plot to visually understand what quadrant you are calculating for.
Vectors
quantities that have both a magnitude and a direction
Scalars
quantities, such as temperature or distance, that are just numbers without any direction
Any two objects in free fall
regardless of their mass, have the same acceleration.
vector addition
the combining of vector magnitudes and directions
An object's acceleration is the slope of its_______
velocity-versus-time graph