part 1 motion in two dimensions scalars a scalar is a quantity that can be completely described by a...
TRANSCRIPT
Part 1 Motion in Two Dimensions
Scalars• A scalar is a quantity that can be completely
described by a single value called magnitude.
• Magnitude means size or amount and always includes units of measurement. Temperature is a good example of a scalar quantity.
Vectors• Sometimes a single number does not
include enough information to describe a measurement.
• A vector is a quantity that includes both magnitude and direction.
Describing a vector
• You can describe a vector three ways;
– With a vector diagram drawn to scale
– As a magnitude-angle pair– As an x-y pair
A vector’s direction
• A vector’s direction is often given using words.
• Directional words include left, right, up, down, north, south, east, and west.
• Which coordinates you use depends on the problem you are trying to solve.
• Sometimes you will make x horizontal and y vertical. Other times, you should choose x to be east and y to be north.
• Velocity is speed with direction, so velocity is a vector.
• As objects move in curved paths, their velocity vectors change because the direction of motion changes.
• The symbol is used to represent velocity.
• The arrow tells you it is the velocity vector, not the speed.
Velocity vector
Velocity vector• Suppose a ball is launched at five meters
per second at an angle of 37 degrees.
• At the moment after launch the velocity vector for the ball is written as = (5 m/s, 37°) or v = (4, 3) m/s.
• Both representations tell you exactly how fast and in what direction the ball is moving at that moment.
• The x-component tells you how fast the ball is moving in the x-direction.
• The y-component tells you how fast it is moving in the y-direction.
Magnitude of the velocity vector• The magnitude of the velocity
vector is the speed of the object.
• The ball in the example is moving with a speed of 5 m/s.
• Speed is represented by a lower case v without the arrow.
• When a velocity vector is represented graphically, the length is proportional to speed.