Question

Regarding the velocity of a particle in uniform circular motion about a fixed axis, select the correct option. w & r angular velocity and radius vectors respectively. ‘X’ & ‘ . ’ represent cross & dot products respectively.

(a) v = r X w

(b) v = w X r

(c) v = w.r

(d) w = v.r

This question was posed to me during an online exam.

This key question is from Vector Product of Two Vectors topic in chapter System of Particles and Rotational Motion of Physics – Class 11

Answer 1

Correct choice is (b) v = w X r

To explain: For a particle rotating about a fixed axis, its angular velocity vector points along the axis. Velocity of a particle is a vector so it will be a cross product and not a dot product. Now if we keep our fingers along the direction of the angular velocity vector and curl them in the direction of the radius we get the direction of velocity for that radius vector. Therefore, v = w X r. Refer to the diagram.