|Centripetal and Centrifugal Force|
|*Plastic bucket with handle
|#Measure your arm from the shoulder to your hand. When spinning the bucket, this will be the radius of the circle. Record the length in meters.
Results: The water will spill out of the bucket when the gravitational force of the water exceeds the centripetal force exerted on the water when it is upside down.
|Centripetal force exerted on a spinning object like our bucket of water also leads to an equal and opposite centrifugal force, an apparent force that draws a rotating object away from the center of rotation (thus holding the water in the bottom of the bucket as it passes overhead). Centrifugal force is a consequence of inertia—the tendency of a moving object to want to continue moving in a straight line. As we fling our bucket of water in an arc over our head, the water wants to continue traveling in a straight line, but our string constantly redirects the water so it travels in an arc instead! Water’s inertia resists this redirection, leading to the apparent force that “pulls” the water into the bottom of the bucket. It’s a great example of Newton’s third law: The string pulls on the water to change its direction from a straight line to an arc (centripetal force), and the water’s inertia pulls back (centrifugal force)!
Here’s an analogous situation: Imagine you’re riding as a passenger in your dad’s car. He makes a really sharp turn, and as a result, you feel like you’re being thrown against the inside of the car door. What’s really happening is that your body wants to continue moving forward, but the turning car pulls your body in a new direction. Your body’s inertia resists this pull, because like all objects, it wants to continue traveling in a straight line.
Now, let’s take a look at the math.
To solve for velocity of your swinging bucket, you have to calculate the gravitational force that acts on the water:
Where Fg is the gravitation force in Newtons, m is the mass of the water and g is the acceleration due to gravity, which is 9.81 m/s on Earth.
The water will spill from the bucket when the gravitational force is slightly greater than the centripetal (or centrifugal) force, so for simplicity they can be set to equal each other, the variables rearranged, and solved. It is important that weight (mass) is measured in kilograms because that the units in the equation must be consistent for the equation to be true.