2.1 - 2.3

Scalars

What type of quantity is described completely by magnitude only, with no direction?

Length, mass, time, temperature, speed

What are examples of scalar quantities?

Vectors

What type of quantity requires both magnitude and direction for a complete description?

Force, position, velocity, moment

What are examples of vector quantities?

Length of arrow

In a graphical representation of a vector, what represents the magnitude?

Angle θ

In a graphical representation of a vector, what represents the direction relative to a reference axis?

Arrowhead

In a graphical representation of a vector, what indicates the sense (which way along the line of action)?

Tail

In a graphical representation of a vector, what is the starting point?

Head

In a graphical representation of a vector, what is the ending point?

Bold letter or arrow notation

What is the standard notation for a vector?

Same direction, magnitude changes

What happens when you multiply a vector by a positive scalar?

Magnitude changes, direction reverses

What happens when you multiply a vector by a negative scalar?

Multiply by a fraction

What is vector division by a scalar equivalent to?

Parallelogram Law

What method of vector addition involves placing tails together and forming a parallelogram?

Triangle Rule

What method of vector addition is a special case of the parallelogram law where vectors are placed head-to-tail?

Commutative property

What property of vector addition allows R = A + B = B + A?

Add magnitudes

If two collinear vectors act in the same direction, how do you find the resultant magnitude?

Subtract magnitudes

If two collinear vectors act in opposite directions, how do you find the resultant magnitude?

Direction of larger magnitude

When subtracting collinear vectors, what direction does the resultant take?

Vector subtraction = addition of the negative

How is vector subtraction defined in relation to vector addition?

Force vector

What type of quantity is a force in statics?

Parallelogram law & triangle rule

What two methods can be used to find a resultant of two forces?

Law of cosines

What trigonometric law is used to find the magnitude of a resultant when two forces and the included angle are known?

Law of sines

What trigonometric law is used to find the direction of a resultant in a force triangle?

Force components

What is the purpose of resolving a force into components?

Parallel to u-axis

When resolving a force, in what direction is the u-component drawn?

Parallel to v-axis

When resolving a force, in what direction is the v-component drawn?

Rectangular components method

What is the preferred method for adding more than two forces acting at a point?

R = √(A² + B² + 2ABcosθ)

What is the formula for the magnitude of the resultant R of two vectors A and B with angle θ between them?

R = √(A² + B² - 2ABcosγ)

What is the formula for the magnitude of the third side R of a triangle given sides A, B and included angle γ?

A/sinα = B/sinβ = R/sinγ

What is the formula relating the sides A, B, R and angles α, β, γ in a vector triangle?

Fu = Fcosθ, Fv = Fsinθ

What are the formulas for the u and v components of a force F at angle θ?

φ (phi) is the final direction of the resultant force F⃗ᵣ measured from the horizontal axis

What is φ (phi) in the context of vector addition?