Question

Does force perpendicular to the velocity change only its direction; not the speed?

While analyzing the case of a force and consequently an acceleration acting perpendicular to the velocity of a given body, I do understand that force's component along the velocity will be 0 causing no change in speed, i.e. magnitude of the velocity (along initial velocity), but will it not add a component in the direction along the force and perpendicular to the velocity.

Even if we assume that at the given instant, the change caused by the acceleration along it does not contribute anything.

Also, if we're neglecting the instantaneous change in magnitude, why then are we accounting the change in direction?

Answer 1

When a force acts perpendicular to the velocity of a body, it only changes the direction of the velocity, not the speed.

Step-by-step explanation:

When a force acts perpedicular to the velocity of a body, it does change the direction of the velocity but not the speed. This can be understood by considering the components of the force along the velocity and perpendicular to the velocity. The component along the velocity is zero, so it doesn't cause any change in speed. However, the component perpendicular to the velocity does contribute to a change in direction.

For example, imagine a ball moving with a constant velocity in the x-direction. If a force is applied in the y-direction, the ball will undergo an acceleration in the y-direction. This acceleration will cause the ball's velocity to change its direction, while the magnitude of the velocity remains the same.