I Electrical potential, II Torque, III Kinetic Energy, IV Momentum. Which of the quantities listed are vectors?

Analyze the question: You need to identify which of the four quantities have both magnitude and direction (vectors) and which have magnitude only (scalars).

Concept:

• A scalar has magnitude only.
• A vector has magnitude and direction.

Going through each quantity:

I. Electrical potential: This is the work done per unit charge (V = W/q). Work is a scalar, so potential is a scalar.

II. Torque: τ = r × F, which is a cross product. It has a direction (along the axis of rotation, given by the right-hand rule). So it is a vector.

III. Kinetic energy: KE = ½mv². It depends on v², so there is no direction. It is a scalar.

IV. Momentum: p = mv. Mass is a scalar and velocity is a vector, so momentum is a vector pointing in the direction of the velocity.

Result: The vectors are II (torque) and IV (momentum).

Exam tip: Energy in any form (kinetic, potential, work, heat) and potential (electric or gravitational) are scalars. Quantities involving force, displacement, velocity, or their cross products (torque, momentum, acceleration, and so on) are vectors. A quick check is to ask, "Does it make sense to say which way it points?" If yes, it is a vector.