Question

A particle is acted upon by a force of constant magnitude is always to the linear velocity of the particle in the case of uniform circular motion.

Answer 1

Uniform circular motion

Uniform circular motion.

1. Uniform circular motion means that the particle or an object or a body which moves or travels in the circular path, with uniform acceleration.
2. Uniform acceleration is the acceleration of the object or body or a particle being constant. There is no increase or decrease in the acceleration.
3. In the figure above, $F$ represents the centripetal force, which always acts towards the center and $v$ is the linear velocity of the particle.
4. If this centripetal force acts on a particle, the linear velocity due to this force is along the tangent to the circular curve, thus, always perpendicular to the direction of that force.
5. As $F=\raisebox{1ex}{$m{v}^2$}\!\left/ \!\raisebox{-1ex}{$r$}\right.$ and $m$is mass of particle while $r$ is the radius of the circle in which particle is revolving.
6. Particle movement occurs in any plane in the cartesian coordinate system. ( $xy$ or $yz$ or $zx$ plane).
7. Linear velocity may vary continuously, as the direction of movement changes its path continuously during circular motion.

Hence, the force acting on a particle always acts perpendicular to the linearvelocity.