Question

When the position vector \[ \vec r = x\hat{i}+y\hat{j}+z\hat{k} \] changes sign as \(\vec r \rightarrow -\vec r\), which one of the following vectors will {not flip under sign change?}

• A. Linear momentum
• B. Angular momentum
• C. Velocity
• D. Acceleration

Hint:

Vector cross products of two vectors that both change sign remain unchanged.

Answer 1

The Correct Option is B

Step 1: Effect of sign change If: \[ \vec r \rightarrow -\vec r \] Then: \[ \vec v=\frac{d\vec r}{dt}\rightarrow -\vec v, \quad \vec a=\frac{d^2\vec r}{dt^2}\rightarrow -\vec a \]
Step 2: Check each quantity
Linear momentum: \[ \vec p=m\vec v \rightarrow -\vec p \] (Sign changes)
Velocity: changes sign.
Acceleration: changes sign.
Angular momentum: \[ \vec L=\vec r\times\vec p \rightarrow (-\vec r)\times(-\vec p)=\vec r\times\vec p \] (Sign unchanged)
Final Answer: \[ \boxed{\text{Angular momentum}} \]