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Force components

A force has both a magnitude and a direction. To calculate with it we split it into a horizontal and a vertical part, called components. Then we can add up forces in each direction separately.

F_x = F\cos\theta

horizontal component (θ measured from the x-axis)

F_y = F\sin\theta

vertical component

F = \sqrt{F_x^2 + F_y^2}

magnitude back from the components

Symbols

$F$	magnitude of the force	N
$\theta$	angle from the x-axis	°
$F_x,\ F_y$	components	N

Example

$F = 200$ N at $\theta = 30^\circ$ :

$F_x = 200\cos 30^\circ \approx 173$ N and $F_y = 200\sin 30^\circ = 100$ N.

Cosine belongs to the side next to the angle, sine to the side opposite it.

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