Newton's second law turned inward

Which statement is Newton's second law?

A ball is whirled on a string, around a horizontal circle at a steady speed. Nothing about the motion looks violent. But the ball is accelerating the whole time, toward the hand at the center.

What does Newton's second law say must exist, for the ball to accelerate like that?

You have seen that an object in uniform circular motion accelerates toward the center at every instant.

You have also seen, in the dynamics topic, that an acceleration never happens on its own: a net force produces it, pointing the same way.

Put the two together.

An object in uniform circular motion always has a net force on it directed toward the circle's center: because the centripetal acceleration points toward the center, Newton's second law (a = F/m) requires a net force in that same inward direction.

This is not a new law. It is the dynamics topic's second law, read along the inward direction.

At this instant, the net force on the ball points at the hand.

The whirled ball's acceleration points at the hand, so the net force on it points at the hand, at every instant.

A quarter turn later, the net force still points at the center.

The steady speed changes nothing. As long as the path is a circle, the net force points inward the whole way around.

Two things you have seen, chained into one inward net force.

A race car laps a flat circular track at a steady speed. In which direction does the net force on it point?

A jogger rounds a flat circular path at a steady pace. Why must there be a net force on her?

A rider on a carousel horse moves in a circle at a steady speed. State the direction of the net force on the rider, and the reasoning.

The rider's centripetal acceleration points toward the carousel's center at every instant.

Newton's second law ties the net force to the acceleration: the two point the same way.

So the net force on the rider points toward the carousel's center at every instant.

The net force on the rider points toward the center, the whole ride.

Luca says: a ball whirled on a string at a perfectly steady speed still has a nonzero net force on it the whole way around. Is he correct?

Your turn

A bus loops a flat circular road at a steady 9 m/s. In which direction does the net force on it point?

A scooter circles a fountain at a steady speed. Which statement about the forces on the scooter is correct?

A toy drone flies a horizontal circle at a steady speed, counterclockwise as drawn from above. At the moment it passes the easternmost point of its circle, in which compass direction does the net force on it point?