Circular Motion What are some examples of objects taking a circular path? What force causes those objects to follow that path?

Circular Motion

Let’s Review First! F=force (N) m=mass (kg) a=acceleration (m/s2) Remember Newton’s 2nd Law… F=force (N) m=mass (kg) a=acceleration (m/s2)

F=ma What is FORCE? A PUSH or a… A PULL

Examples of Forces Tension Friction Gravity Impact Forces

F=ma MASS The amount of MATTER an object contains. This stays constant. Not weight - weight changes depending on gravitation field

How the velocity changes in a certain amount of time F=ma ACCELERATION How the velocity changes in a certain amount of time In physics lingo a=acceleration (m/s2) Δ= “change in” v=velocity (m/s) t=time (s)

What is Circular Motion? Uniform Circular Motion: movement of an object at a constant speed around a circle with a fixed radius

Examples Rollercoaster Swinging an object on a string Planetary objects - moon, satellites, etc. Car going around a round-about

Circular Motion and Force If an object stays in its path… It must have a net force – remember Newton’s 1st Law… This force is called… CENTRIPETAL FORCE centrum: "center" and petere: “go to” or “seek” So, it’s a “center – seeking” force

Examples of these “acting” as the This is not a new force !! Examples of forces: Gravity Impact Forces Examples of these “acting” as the CENTRIPETAL FORCE Planetary Motion Rollercoaster Tension Friction Ball on a string Car going in circles

Centripetal Acceleration is… The acceleration of an object in uniform circular motion. The ac always points toward the center.

Finally put it all together… So, for centripetal force…

Remember The circumference of a circle C = 2πr r measured in METERS r

Using Period, T, to find velocity The time it takes an object to make a complete revolution is the PERIOD. During this time, it travels a distance equal to the circumference of the circle Remember, v = ∆d/∆t So, v = 2πr/T

What happens when the force is no longer acting What happens when the force is no longer acting? (Think Newton’s 1st Law)

“Critical Velocity” Is the minimum/maximum velocity needed to maintain the circular path You can consider vertical motion (like a satellite) or horizontal motion (like a car) For example, what is the fastest you can go around a curve in your car without losing control; or, what is the minimum speed a satellite needs to stay in orbit?

How many g’s? The g-force references the acceleration of the object relative to free-fall To determine the number of “g’s” an object experiences, you divide the object’s acceleration by acceleration due to gravity (9.8 m/s2) – it’s a ratio “g’s” = a/9.8

What to remember What circular motion is - recognize it!!! Newton’s Second Law: F = ma Velocity can be calculated from period: v = 2πr/T Centripetal acceleration depends on the object’s velocity and distance from the center of its path Centripetal force are mass, velocity, and the distance from the center of the path (radius)

Let’s do some Calculations What is an object’s centripetal acceleration if it travels 22 m/s around a circular path with a 0.12 m radius? An object has a mass of 50 kg, travels in a circular path of radius 1.2 m and rotates 150 revolutions per minute. Find the object’s velocity What is the centripetal force on the object?