Which of the following physical quantities is a vector quantity rather than a scalar quantity?

Introduction / Context:

This question tests the understanding of the difference between scalar and vector quantities in physics. Scalars have magnitude only, whereas vectors have both magnitude and direction. Being able to classify physical quantities correctly is essential for setting up equations of motion, torque, rotational dynamics, and energy calculations.

Given Data / Assumptions:

• The options include heat, angular momentum, work, and time.
• We must identify which quantity is a vector.
• Standard school level definitions of these quantities are assumed.
• Direction and sign conventions follow usual physics usage.

Concept / Approach:

Heat, work, and time are scalar quantities. They have magnitude but no intrinsic direction in space. For example, time flows forward, but it is not treated as a vector in mechanics. Anglular momentum, on the other hand, is a vector quantity related to rotational motion. It has a magnitude and a direction given by the right hand rule, perpendicular to the plane of rotation. Thus, among the given options, angular momentum is the only vector quantity.

Step-by-Step Solution:

Verification / Alternative check:

Mathematically, angular momentum L is defined as r cross p, where r is position vector and p is linear momentum vector. The cross product of two vectors is always a vector, confirming that angular momentum is a vector. In contrast, heat and work are measured just by magnitudes in joules. Laws of addition for heat and work are simple algebraic addition, not vector addition. Time is not represented by arrows in space diagrams, reinforcing that it is scalar.

Why Other Options Are Wrong:

• Heat: Scalar quantity with units of joule, representing energy transfer, no direction in space.
• Work: Scalar quantity equal to force component along displacement times displacement, also in joules.
• Time: A scalar parameter that orders events but is not treated as a vector in mechanics problems.

Common Pitfalls:

Students sometimes think any quantity that can be positive or negative must be a vector, which is not correct. Scalars like work can be negative, but they still have no associated spatial direction. Another confusion is between momentum and angular momentum. Both are vectors, but this question includes only angular momentum. Recognising definitions and how quantities appear in vector equations is the safest way to classify them correctly.

Final Answer:

Angular momentum is the vector quantity among the given options.