First slide

Scalars and 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^o 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

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

Solution

In new coordinate system,
$\begin{array}{l} F \sin 37^{\circ} = 6 N \\ F \cos 37^{\circ} = 8 N \\ x -component F_{x} = F \sin 37^{\circ} = 10 \times \frac{3}{5} = 6 N \end{array}$
$y -component F_{y} = - F \cos 37^{\circ} = - 10 \times \frac{4}{5} = - 8 N$

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