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Welcome back to Physics 211. Today’s agenda: Review Vectors Vector components. ConcepTest 8. You are throwing a ball…. Acceleration of ball rolling on incline. Acceleration is not zero at top. velocity. time. Vectors. are used to denote quantities that have magnitude and direction

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welcome back to physics 211

Welcome back to Physics 211

Today’s agenda:



Vector components

conceptest 8

ConcepTest 8

You are throwing a ball…

  • are used to denote quantities that have magnitude and direction
  • can be added and subtracted
  • can be multiplied or divided by a number
  • can be manipulated graphically (i.e., by drawing them) or algebraically (usually by considering components)
  • Numbers: temperature, pressure, volume ….
  • Vectors: position, velocity, force
adding vectors

Adding vectors

To add vector B to vector A:

Draw vector A.

Draw vector B with its tail starting from the tip of A.

The sum vector A+B is the vector drawn from the tail of vector A to the tip of vector B.


Two unknown vectors A and B are added.

The magnitude of the sum vector “A + B” (i.e., the quantity |A + B|)

1. is at least as great as |A| (i.e., the magnitude of A).

2. is at most as great as |A| + |B| (i.e., the magnitudes of A and B added).

3. must be equal to |A| + |B|.

4. can be greater than |A| + |B|.

projection of a vector

Projection of a vector

Component of a vector

“How much a vector acts along some arbitrary direction”

Projection onto one of the coordinate axes (x, y, z)








i unit vector in x direction



j unit vector in y direction

ax,ay components of vector A

Projection of A along coordinate axes

more components
More components
  • Note:

ax=|A|cosq, ay=|A|sinq

  • |A|2=ax2+ay2
why components useful
Why components useful ?
  • Addition: just add components

if C=A+B

cx=ax+bx; cy=ay+by

  • Magnitude |A|2=ax2+ay2
  • Direction tanq=ay/ax

A bird is flying along a straight line in a direction somewhere East of North. After the bird has flown a distance of 2.5 miles, it is 2 miles North of where it started.

How far to the East is it from its starting point?

1. 0 miles

2. 0.5 miles

3. 1.0 mile

4. 1.5 miles

2d motion
2D Motion


component of position vector

along x direction is the x coordinate!

s – vector position



Describing motion with vectors

  • Positions and displacements

s,Ds = sfinal - sinitial

  • Velocities and changes in velocity:

vave= ––––,vinst= lim ––––,

Dv = vfinal - vinitial

  • Acceleration: aave= ––––,ainst= lim ––––,



quick quiz 3 3 from serway beichner physics
Quick Quiz 3.3(from: Serway/Beichner, Physics)

Can any component of a vector ever be greater than the magnitude of the vector?

1. Yes

2. No

3. Not sure

quick quiz 3 4 from serway beichner physics
Quick Quiz 3.4(from: Serway/Beichner, Physics)

If one component of a vector is not zero, can the magnitude of the vector be zero?

1. Yes

2. No

3. Not sure