A vector of magnitude 10 N acting in X Y-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° in anti-clockwise direction. Find x-component and y-component in new coordinate system.

Question

A vector of magnitude 10 N acting in X Y-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° in anti-clockwise direction. Find x-component and y-component in new coordinate system. (A) Fx=8 N , Fy=6 N (B) Fx=6 N , Fy=8 N (C) Fx=6 N , Fy=-8 N (D) Fx=8 N , Fy=-6 N

Tardigrade Admin · Accepted Answer

In new coordinate system,

F sin 37°=6 N F cos 37°=8 N x-component Fx=F sin 37° =10 × (3/5)=6 N

y-component Fy=-F cos 37° =-10 × (4/5)=-8 N

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

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

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

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

In new coordinate system,

$F sin 3 7^{\circ} = 6 N$
$F cos 3 7^{\circ} = 8 N$
$x$ -component $F_{x} = F sin 3 7^{\circ}$
$= 10 \times \frac{3}{5} = 6 N$

$y$ -component $F_{y} = - F cos 3 7^{\circ}$
$= - 10 \times \frac{4}{5} = - 8 N$

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

Fx​=8N,Fy​=6N

Fx​=6N,Fy​=8N

Fx​=6N,Fy​=−8N

Fx​=8N,Fy​=−6N

In new coordinate system, Fsin37∘=6N Fcos37∘=8N x-component Fx​=Fsin37∘ =10×53​=6N y-component Fy​=−Fcos37∘ =−10×54​=−8N

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

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

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

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

In new coordinate system,

$F sin 3 7^{\circ} = 6 N$
$F cos 3 7^{\circ} = 8 N$
$x$ -component $F_{x} = F sin 3 7^{\circ}$
$= 10 \times \frac{3}{5} = 6 N$

$y$ -component $F_{y} = - F cos 3 7^{\circ}$
$= - 10 \times \frac{4}{5} = - 8 N$