A model train runs counterclockwise around a circular track at a steady speed, viewed as drawn on the page. Two photographs catch it at two nearby points, a moment apart.
The acceleration points the way the velocity changes. Subtract the two velocity arrows, and see which way the change points.
Acceleration points in the direction of the change in velocity.
Take the train's velocity arrow in the first photograph, and its velocity arrow in the second. Both arrows have the same length, because the speed never changed.
Their directions differ a little, because the track has turned the train.
To see the change, place the two tails together. The change is the arrow that joins the tip of the earlier arrow to the tip of the later one.
Draw that joining arrow, and it points inward, toward the center of the circle.
Slide the pair of photographs to any other part of the circle and repeat the subtraction. The joining arrow aims at the center every time.
That is why the acceleration in uniform circular motion is centripetal at every instant.
An object moves around a circle at a steady speed. Between two nearby points on its path, which way does the change in its velocity point?
A drone flies a circle at a steady speed, and its acceleration points toward the center. Why?
The train runs counterclockwise. The first photograph catches it at the circle's 12 o'clock position, the second a moment later, just past it. Which way does the change in velocity point?
At the 12 o'clock position the velocity sits on the horizontal tangent, pointing left (counterclockwise carries the train from the 12 position toward the 9).
A moment later the train sits just past the 12, and its tangent has tilted: the velocity points left and slightly downward.
Place the tails together. The arrows match in length and differ slightly in direction.
The tip-to-tip joining arrow points downward: from the top of the circle toward the center.
The change in velocity points downward, toward the center.
The same counterclockwise train, photographed at the 3 o'clock position and a moment later. Which way does the change in velocity point?
At the 3 o'clock position the velocity sits on the vertical tangent, pointing up (counterclockwise carries the train from the 3 position toward the 12).
A moment later its tangent has tilted: the velocity points up and slightly leftward.
Place the tails together, and join tip to tip.
The joining arrow points leftward: from the 3 o'clock position toward the center.
The change in velocity points leftward, toward the center.
Two velocity arrows from nearby moments are placed tail to tail. Which arrow is the change in velocity?
A gondola rides a Ferris wheel at a steady rate. Which statement explains why its acceleration points toward the wheel's center?
Viewed as drawn on the page, a cart runs counterclockwise around a circle. Its velocity arrows at the 3 o'clock position and at a nearby later moment are placed tail to tail, and the tip-to-tip arrow is drawn. The circle's center lies to the left of the 3 o'clock position. Which way does the tip-to-tip arrow point?
As an object travels all the way around its circle at a steady speed, what happens to the direction of its acceleration?