Which statement correctly identifies the angular momentum of a particle about a point?

Which statement correctly identifies the angular momentum of a particle about a point?

• A. angular momentum of a rigid body
• B. angular momentum of a particle
• C. angular velocity
• D. angular acceleration

Answer: (B)

Angular momentum about a point for a particle is defined as L = r × p, where r is the position vector from the chosen point to the particle and p is the particle’s linear momentum (p = m v). The magnitude is L = m r v sin(theta), with theta the angle between r and v, and its direction is perpendicular to the plane formed by r and v (given by the right-hand rule). This directly captures the rotational effect of that single particle about the reference point, which is exactly what the statement in question is identifying. The other rotational quantities—angular velocity (how fast something is rotating) and angular acceleration (how the rotation rate changes)—are not angular momentum themselves. While you can define angular momentum for a rigid body about a point by summing contributions from all particles, the phrase here specifies the particle case, so the particle-focused definition is the appropriate one.

Angular momentum about a point for a particle is defined as L = r × p, where r is the position vector from the chosen point to the particle and p is the particle’s linear momentum (p = m v). The magnitude is L = m r v sin(theta), with theta the angle between r and v, and its direction is perpendicular to the plane formed by r and v (given by the right-hand rule).

This directly captures the rotational effect of that single particle about the reference point, which is exactly what the statement in question is identifying. The other rotational quantities—angular velocity (how fast something is rotating) and angular acceleration (how the rotation rate changes)—are not angular momentum themselves. While you can define angular momentum for a rigid body about a point by summing contributions from all particles, the phrase here specifies the particle case, so the particle-focused definition is the appropriate one.