1.1.3 Adding and resolving vectors Flashcards by Nirwan Gayathra

Q

Scalar quantity

A

Quantity with magnitude only

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Q

Vector quantity

A

Quantity with magnitude and direction

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Q

Examples of scalar

A

Distance, speed, time

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Q

Examples of vector

A

Displacement, velocity, acceleration, force

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Q

How are vectors represented?

A

Arrows (length = magnitude, direction = arrowhead)

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Q

What does the length of a vector represent?

A

Magnitude

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Q

What does arrow direction represent?

A

Direction

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Q

Resultant vector

A

Single vector that represents the sum of multiple vectors

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Q

How to add vectors (diagram method)

A

Head-to-tail method

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Q

Resultant vector (addition)

A

Drawn from tail of first to head of last vector

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Q

How to subtract vectors

A

Reverse direction of vector then add

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Q

What is −B?

A

Same magnitude as B but opposite direction

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Q

What is meant by coplanar vectors?

A

Vectors in the same plane

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Q

When vectors cancel out

A

Resultant = 0

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Q

Condition for equilibrium

A

Resultant force = 0

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Q

What does equilibrium mean?

Study These Flashcards

A

No net force, object at rest or constant velocity

Q

Closed triangle rule

Study These Flashcards

A

Used for equilibrium (vectors form closed shape)

Q

What is a vector component?

Study These Flashcards

A

Part of a vector in a specific direction

Q

Why resolve vectors?

Study These Flashcards

A

To simplify calculations in perpendicular directions

Q

Horizontal component formula

Study These Flashcards

A

F cosθ

Q

Vertical component formula

Study These Flashcards

A

F sinθ

Q

Which uses cosθ?

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A

Adjacent component

Q

Which uses sinθ?

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A

Opposite component

Q

Vector in i-j form

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A

F = (Fx)i + (Fy)j

Column vector form

(Fx, Fy)

Magnitude of a vector from components

√(Fx² + Fy²)

Direction of vector

θ = tan⁻¹(Fy / Fx)

What is resolving a vector?

Splitting into perpendicular components

When resolving on slope

Parallel = mg sinθ, perpendicular = mg cosθ

Sign convention (right/up)

Positive

Sign convention (left/down)

Negative

How to find resultant using components

Add horizontal and vertical separately

Resultant magnitude formula

√(Rx² + Ry²)

Resultant direction formula

tan⁻¹(Ry / Rx)

When to use Pythagoras

Perpendicular vectors

When to use trigonometry

Angled vectors

What does bearing mean?

Direction measured clockwise from north

What is “north-east” direction?

45° from north