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.