How are radius, velocity, acceleration, and force related in circular motion?

Many objects—from spinning wheels to the orbits of satellites around the Earth—undergo circular motion. For an object to remain in circular motion, it must experience a centripetal force (and acceleration). In this investigation, you will explore the properties of circular motion at scales similar to that of a mass swung around horizontally at the end of a string.

Part 1: Directions of the velocity, force, and acceleration vectors

Set m = 5.0 kg, r = 5.0 m, and v = 5.0 m/s.

Play the simulation, and then pause it at various positions around the circle.

Sketch the velocity, force, and acceleration vectors for at least five positions distributed around the circle.

Which vector quantity or quantities are radial and which are tangential? Are the radial quantities pointed inward (toward the center) or outward?

Do the lengths of the velocity, acceleration, or force vectors change around the circle?

Notice that the angular velocity is exactly 1 rad/s. Why?

In this interactive simulation, you will investigate how velocity, acceleration, and force vary when an object is undergoing circular motion.

Part 2: Approximating a mass swung overhead

Set r = 1.0 m and m = 0.3 kg.

Calculate the tangential velocity needed to spin the object around once per second, and enter that into the simulation.

How much force is needed to maintain this object in circular motion?

Compare that force with the force required to hold the object motionless against the force of gravity.

Lengthen the string to r = 2.0 m. Does it now require more or less force than before to maintain the object in circular motion with the same angular velocity?

Part 3: Variation of velocity with radius for circular motion

Hold the force constant at 10 N and the mass constant at 2 kg, but vary the length of the string from r = 1 m to 5 m.

Record the velocity and radius for each case.

Graph v (on the vertical axis) against r and describe the shape of your graph.

Graph v^{2} against r, describe the shape of your graph, and measure its slope (including units).