Golda is labeling a diagram of a ball circling on a string: the circle, the center, the ball at the 3 o'clock position. She needs to add the acceleration arrow.
One rule fixes the arrow at any point. Where does it aim?
Step 1: find the center of the circle on the diagram.
Step 2: draw the line from the object's position to the center.
Step 3: put the arrow's tail at the object, and aim its head at the center, on that line.
At the 3 o'clock position, the center lies to the left, so the arrow points left toward the middle.
Golda's ball is at the 3 o'clock position of its drawn circle, the center marked at the middle. Draw the centripetal acceleration arrow.
Find the center: the marked middle of the circle.
Draw the line from the ball at the 3 o'clock position to the center: it runs horizontally.
Tail at the ball, head aimed at the center.
The arrow points left, from the ball toward the middle.
The satellite circles at a steady speed and is at the 12 o'clock position shown. Which way does its centripetal acceleration arrow point?
The runner rounds the track at a steady speed and is at the 9 o'clock position shown. Which way does her centripetal acceleration arrow point?
The sense of travel never enters the routine. Clockwise or counterclockwise, the acceleration arrow aims at the center either way.
That makes the acceleration arrow easy to check: its line must pass through the center. An arrow that misses the center is drawn wrong.
Remember which arrow this is: the velocity rides the tangent, and the acceleration rides the radius line, inward.
A different diagram: a cart at the 6 o'clock position of its circle, the center marked. Draw the centripetal acceleration arrow.
Find the center: directly above the cart on this diagram.
Draw the line from the cart to the center: it runs vertically.
Tail at the cart, head aimed at the center.
The arrow points straight up, from the cart toward the center.
A bead circles a drawn circle, and its centripetal acceleration arrow has been drawn correctly at the 6 o'clock position. The bead's sense of travel is now reversed, everything else unchanged. Does the acceleration arrow change?
The swing ride turns clockwise, viewed as drawn on the page, and the rider is at the 12 o'clock position shown. Which way does the rider's centripetal acceleration arrow point?
The boat circles counterclockwise, viewed as drawn on the page, and is at the 3 o'clock position shown. Which way does its centripetal acceleration arrow point?
The pony circles at a steady speed and is at the 9 o'clock position shown. Which description gives its correct centripetal acceleration arrow?