Resolving a Vector Into Perpendicular Components (Leaving Cert Physics): Flashcards

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Resolving a Vector Into Perpendicular Components
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What is vector resolution?

Breaking a vector into component vectors

Vector resolution is the reverse of

Finding resultant using parallelogram law

Angle between perpendicular components

90° (right angles)

Formula: horizontal component (r at angle θ)

x=rcos⁡θx = r \cos θ

Formula: vertical component (r at angle θ)

y=rsin⁡θy = r \sin θ

SOH CAH TOA: meaning of CAH

Cosine = Adjacent / Hypotenuse

SOH CAH TOA: meaning of SOH

Sine = Opposite / Hypotenuse

Formula: original vector magnitude from x, y

r=x2+y2r = \sqrt{x^2 + y^2}

Formula: angle of resultant from x, y

θ=tan⁡−1(yx)θ = \tan^{-1}(\frac{y}{x})

Application: breaking initial velocity into components

Projectile motion

Application: separating weight on a slope

Forces on inclined planes

Can perpendicular components be analyzed separately?

Yes, they are independent

How do components compare to original vector?

Components are smaller than (or equal to) original

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