object on vertical circle
- Dennis Fort
For Radhika: This is a diagram illustrating some of the unit problems we talked about. I made this to match one of your homework problems. Vector Diagram for an object moving around a vertical circle. The circle radius R = 23 m. The speed of the object is 15.6 m/s. The vectors shown are due to gravity (vector g), centripetal acceleration (vector ac). The vector g always points in the negative y direction. The vector ac always points toward the center of the circle. If the object traveling around the circle is a car, the question might be how much acceleration is felt by a person inside the car, and what is the magnitude and direction of that acceleration. The red vector (vector a) shows the answer. The easiest way to find it is to make ac point in the opposite direction (away from the center) and then add it to vector g. It takes a little explaining to understand why you do it that way, but for now, it's best to just remember it. The red vector magnitude and direction will depend on where the car is on the circle. The two easiest points on the circle to find it are the top and bottom. At the bottom, the magnitude of a = g + ac and the direction is straight down. At the top, the magnitude of a = g - ac and the direction is straight down if g > ac or straight up if g < ac.
If you put the mouse on the point C, then right click and drag, you can move the point around the circle and see how the vectors change. Notice that vector g is always the same and pointing straight down. Vector ac is always the same size and points toward the center. Vector a (the red one) represents the total acceleration felt by a person riding in the car, and changes all around the circle.