When the position vector r = xi + yj + zk changes sign as −r, which one of the following vector will not flip under sign change?

Q. When the position vector r = x i + y j + z k changes sign as −r, which one of the following vector will not flip under sign change?

1. Velocity

2. Linear momentum

3. Acceleration

4. Angular momentum

Correct Answer: Angular momentum

Solution

Velocity, linear momentum, and acceleration are polar vectors. When the position vector changes sign, polar vectors also change sign.

Angular momentum is defined as:

L = r × p

Both position vector r and linear momentum p change sign under inversion. Since angular momentum is the cross product of two polar vectors, the sign changes cancel.

Therefore, angular momentum remains unchanged. Such vectors are called axial vectors or pseudo vectors.

Hence, the vector that does not flip under sign change of position vector is angular momentum.

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