Physics intro

What is scalar?

Has a size only: a number and a unit

For example: Mass, time, temperature, distance, speed, energy

What is vector?

Has a size and direction

For example: Displacement, velocity, acceleration, force

Is 60 mi/h a scalar or vector?

Scalar (it's speed, no direction)

Is 60 mi/h east a scalar or vector?

Vector (it's velocity, it has a direction)

Distance

Length of the path you actually walked. A scalar.

Displacement

Straight arrow from start to finish. A vector.

Diameter

Straight line across a circle through its center. Circumference (all the way around) = πd

Can a magnitude be negative?

No, never. Magnitude |A| is a length.

Can a component be negative?

Yes. Negative when the vector points left (−x) or down (−y).

Calculator trap with tan⁻¹

tan⁻¹ only gives angles between −90° and 90°. If Ax is negative, add 180°. Always sketch to check the quadrant.

What is î

î is the x component

What is ĵ?

ĵ is the y component

What is k̂

k̂ is the z component

Adding in scalar notation

A + B = (Aₓ + Bₓ) î + (Aᵧ + Bᵧ) ĵ

Subtracting in scalar notation

A - B = (Aₓ - Bₓ) î + (Aᵧ - Bᵧ) ĵ

Circumference Formula

πd
Halfway around is πd/2

How much is 1km in m?

1000m

What is 1m in cm?

100cm

What is 1 hour in minutes and seconds?

60 minutes

3600s

Convert 5km to meters

5km x (1000m / 1km) = 5000m

Convert 72km/h to m/s

• 72km/h has two unit change: km → m and h → s

• 72km/1hr x (1000m/1km) x (1h / 3600s)

• 20 m/s

A drone flies 120 m at 30.0° north of east, then 80.0 m due north. Find its

displacement.

 1. Sketch it, with +x east and +y north.

 2. A = (120 cos 30.0°) î + (120 sin 30.0°) ĵ = (103.9 î + 60.0 ĵ) m

 3. B = (0 î + 80.0 ĵ) m

 4. R = A + B = (103.9 î + 140.0 ĵ) m

 5. R = √(103.92 + 140.02) = 174 m, θ = tan−1(140.0 / 103.9) = 53.4°

north of east

 6. Check: R points up and right like the sketch, and 174 m is less than

120 m + 80.0 m.

1. A dog runs 3 blocks east, 2 blocks north, 1 block east, 1 block north, then

2 blocks west. Each block is about 100 m. How far from home is the dog,

and in what direction? Draw it tip to tail, then check with components

The dog’s displacement is 360.6 m at 56.3 degrees north of east.

A = (2.0 î − 3.0 ĵ) m and B = (−4.0 î + 1.0 ĵ) m. Find A + B and A − B in

unit-vector notation, then the magnitude and direction of each. Sketch

both.

3. If you finish: can a vector have a negative magnitude? Can a component

be negative? If A and B are perpendicular, what is the component of B

along A?