Change in kinetic energy when force is perpendicular to velocity I am a high school student and a have a fundamental doubt.
It is said that when force is applied perpendicular to velocity, there is no change in kinetic energy since there is no change in speed. For change in kinetic energy to happen, the resultant force should have a tangential component.
My question is, if a particle moving horizontally with some speed $V_x$ and a force acts along $y$ axis to increase its speed vertically from $0$ to $V_y$. Isn't the total speed now $√(V^2_x + V^2_y)$ Thus the speed has increased and so should kinetic energy. Please explain where I am going wrong.
 A: The perpendicular component of a force will never change the speed.  This is true.
What is happening in your case is at the instant that the force along the y-axis is applied, it will, for that short, differentially small time, only change the direction of velocity slightly upwards, but have no effect on the speed. However, if the force keeps acting upwards -- and now the object has a velocity component in the upwards y-direction -- the force is no longer perpendicular (there is a tangential component) and thereby the speed will change.
The force's direction would also need to change in such a way that it always remains perpendicular to the object's velocity. An example of this is uniform circular motion.
A: It is said that when force is applied perpendicular to velocity, there is no change in kinetic energy since there is no change in speed.
Exactly what happens when there is uniform circular motion.
System => object undergoing uniform circular motion.
The only force which is acting is the force causing centripetal acceleration whose direction is at right angle to the direction of the velocity so no work is done on the object by the force causing the centripetal acceleration,
My question is, if a particle moving horizontally with some speed $V_{\rm x}$ and a force acts along $y$-axis . . . .
System => the projectile
No force in the horizontal direction, thus no change in the horizontal component of velocity, and a downward gravitational attractive force which does work on the projectile which in turn changes its downward component of velocity had hence its kinetic energy.
