Transcript Kinematics in 2 Dimensions Vectors

Kinematics in 2 Dimensions
Vectors
Vectors and Scalars
• Vector quantities are those that have
both direction and
magnitude…velocity, acceleration,
force, displacement, etc…
• Scalar quantities are those that have
only magnitude…speed,
distance…etc…
What is a vector?...
• A vector is represented as an arrow.
• Multiple vectors should be pointed in the
relative direction that the real vector points
and be proportional to the scale of size
consistent with other vectors present.
• A vector can be moved anywhere in a model
as long as it maintains direction and
magnitude.
Vector Operations
• Vectors can be added by placing them head to
tail until all are drawn…the resultant is a final
vector drawn from the original beginning
point to the final vector arrow-tip.
• To subtract vectors reverse its direction 180o
and draw it …finish as before.
• To multiply a vector by a number, 2 for
instance, double its size… to divide, change
the magnitude, but maintain direction.
Vector Operations….(cont’d)
• When vectors are drawn to scale, you can use
a ruler to measure the resultant and a
protractor to measure the angles. This is
called graphical resolution.
• When you have values in a model, but do not
use a ruler, you can use math to solve for a
resultant…when the vectors are at right
angles, you can use the Pythagorean theorem.
Components of Vectors
• When vector addition cannot be used or is not
accurate enough, resolve each vector into its x
and y components and add the xs and ys at
the end…construct a single x and single y
vector that represent the problem and draw
your resultant. You can use the Pythagorean
theorem since the vectors are at a right angle.
Homework
• Page 70 problems 1-5, 8,9,17