# Circular Motion

and Gravitation

Reference - Forumla Sheet

## Content Overview

Activities

Bowling Ball and Broom - How to push on a bowling ball to keep it moving in a circular motion (alternatively kicking a floating air puck instead of a bowling ball)

Fish Tank Go Round - Observe what happens with the water inside a fish tank as it spins around

Spin Me Right Round - Whirl a mass with a string in a test of the qualitative relationship between orbital velocity, radius, and gravity

What Are You Sinking About? - Where will the containers go when a floating and sunken container are spun in a circle?

My Solar System - PhET Simulation to observe orbits and their characteristics

(With Extra Time) Angular Momentum & Conservation of A. M. Stations - spinning batons, rattleback toy, gyroscope, bicycle wheel on platform, figuring skating spin in a chair, race of two different mass-distributed wheels

Topics

Centripetal Acceleration & Force

Centripetal Force

Frames of Reference

Newton's Law of Universal Gravitation & Orbits

## Students are Expected to Understand

Requirements and Constraints for Maintaining Circular Motion

Perspectives on Centripetal and Centrifugal Forces

Gravity's Effects on Orbits and Motion

Inverse Square Relationships with Regards to Distance and Gravitational Force

### Some Notes on Circular Motion

• Inertia does its best to have all objects moving at a constant velocity. This also means these objects keep moving in a straight line. If you want to make an object move in a circle, you have to keep pushing on the object, and you'll have to continuously push in towards the middle of the circle that the object is moving along
• What happens to objects that don't have that push towards the middle any more? Think about what inertia does to all objects without a net force on them
• A centripetal force is whatever force that's pushing towards a middle of a circle that keeps the object moving in a circle
• However, a centrifugal force is a force that seems to push objects away from the middle. Now, if you're inside a turning or spinning object or if you yourself are being spun, you're definitely feeling it. Think of what it's like to be inside a car that's making a hard turn. You can feel yourself getting pushed towards one of the doors! But if you're looking from the outside in, you would see that you're really just trying to move straight like inertia wants you to, and that straight line happens to be up against the car doors. So depending on how you see things, they're both different and right!
• No orbits are truly circular. In fact, they're all elliptical. Think of it as a type of oval or kind of like the shape of an egg (side note: the word oval comes from the earlier word for "egg")
• The closer an orbiting object is to whatever it is orbiting, the faster it will move. This is because gravity increases significantly with shorter distances and is explained by Newton's Law of Universal Gravitation which helps us understand the inverse square rule with distance and force
• When the International Space Station is passing above us, we're closer to those astronauts than we are to Los Angeles. Astronauts in the ISS experience 90% of Earth's Gravity, so how can they be considered weightless? It's not just about where they are, it's also about how they're moving. They're in orbit meaning that they're being thrown sideways instead of being thrown downward. As long as the space station they're in is also moving sideways with the astronauts, they'll never feel like they're being pushed into the floor. They feel like they're floating! This is also why it can be referred to as microgravity even though there's still plenty of it up there

After studying the pattern behind moving things, we begin looking into what causes things to move. Forces is also an important foundation unit that later topics will rely on. Forces may also be referred to as Dynamics.

*These videos are to be used as a support and are not a replacement for in-class experiences

# Centripetal Force

A bucket of water is spun above someone's head. This force pushes inward towards the middle of the circle. In this case, the water is being pushed by the bucket towards the person spinning it. Why doesn't the water fall onto the person's head when directly above, especially since the water is being both pulled down by gravity and pushed down by the bucket? Turns out that while the force applied to the water is toward the person, the velocity of the bucket is not in that same direction. Something to think about.

# Centrifugal Force

Frequently called a "fictitious force"

# Orbits

Notice in the image which planets are moving fastest. Why would those planets need to move faster? What would happen if they moved much slower?

While the image here is not entirely accurate, it's brings up an interesting idea: Does the Sun orbit anything? And yes, the Sun orbits the center of our galaxy the Milky Way, and this is a fun take on that thought, showing orbits within orbits.

# Gravitational Assist

Also known as a gravitational slingshot

Check out the animated image trajectory of Voyager 2, a satellite to investigate the deepest reaches of our Solar System. To save on time and fuel, they got help by stealing some of the motion of Jupiter and Saturn to be the only spacecraft to visit Uranus and Neptune.

Using gravity from a really massive object like a planet, an object can slingshot itself by getting sucked in by a planet's gravity and shot back out the other side. Imagine someone tossing you a pair of headphones only for you to catch the headphones by the cord and swing them around, yeeting them across the room

After swinging around a planet, doesn't the same planet pull the object back towards itself cancelling any velocity gains? If the object were to make a 180 degree u-turn, yes. However, it's angled so that there is minimal reduction in getting slowed down by pulling back. We will cover more of this when we get to Work during our Energy unit