Question

A vector of magnitude 10 Newton acting in xy plane has component 8 Newton and 6 Newton along positive x axis and positive y-axis respectively the co-ordinate system is rotated about Z Axis through an angle 90 degree in anticlockwise direction find X component and Y component in new co-ordinate system

Answer 1

Answer:

X component and Y component in new co-ordinate system is 6 N and -8 N.

Explanation:

Given that,

Force in xy plane = 10 N

Force in x axis = 8 N

Force in y axis = 6 N

Angle = 90°

The component of the co-ordinate system

X component,

$F_{x}=F\cos\theta$

$F_{x}=8\ N$

Y component,

$F_{y}=F\sin\theta$

$F_{y}=6\ N$

When, the co-ordinate system is rotated about Z Axis through an angle 90 degree in anticlockwise direction

We need to calculate X component and Y component in new co-ordinate system

$F_{x}= F\sin\theta$

$F_{x}=6\ N$

$F_{y}=F\cos\theta$

$F_{y}=-8\ N$

Hence, X component and Y component in new co-ordinate system is 6 N and -8 N.

Answer 2

Answer: New x component is 6 and new y component is -8

Explanation:

Let the vector be named r

In original frame of reference :

r = 8 i + 6 j

When the coordinate frame is rotated through 90° in anti-clockwise direction along Z-axis , following things occur:

• New x gets aligned with original y.
• New y gets aligned with - x.

Therefore,

Original i ⇒ New - j

Original j ⇒ New i

Substituting older coordinates in terms of new coordinates :

Original r = 8 i + 6 j

In new frame of reference :

r = 8 (-j) + 6 i

r = 6 i - 8 j

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