First slide

Vectors

Question

A vector of magnitude 10 N acting in XY-plane has components 8 N and 6 N along positive X-axis and positive Y-axis, respectively. The coordinate system is rotated about z-axis through angle $90^{0}$ in anti-clockwise direction. Find x-component and y-component in new coordinate system.

Moderate

A

$F_{x} = 8 N, F_{y} = 6 N$
B

$F_{x} = 6 N, F_{y} = 8 N$
C

$F_{x} = 6 N, F_{y} = - 8 N$
D

$F_{x} = - 6 N, F_{y} = 8 N$

Solution

In new coordinate system,
$Fsin 37^{0} = 6 N$
$Fsin 37^{0} = 6 N$
$Fcos 37^{0} = 8 N$
x-component $F_{x} = F \sin 37^{0} = 10 \times \frac{3}{5} = 6 N$
New coordinate system
y-component $F_{y} = - Fcos 37^{0}$
= $- 10 \times \frac{4}{5} = - 8 N$

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