1. Circular Motion Centripetal and Centrifugal forces

2. Circular vs. Angular Motion Angular motion is spinning around an internal axis, or rotating It requires NO force to KEEP something spinning once it is spinning. (Rotational inertia; like the earth, tends to keep spinning)

3. Circular Motion Revolving around an EXTERNAL axis DOES require a net external force (CENTRIPETAL) to cause an object to do this (F c = m a c ) Special case of which law? (An object naturally tends to either stay at rest or travel in a straight line! Which law?)

4. Centripetal Force “Center-seeking” ALWAYS toward the center A REAL force with action/reaction pair and a SOURCE providing the force MUST have this force to make something go in a circle link

5. Centripetal force Must have centripetal force provided by ______________ to make your car go around a curve Otherwise, your car will naturally _________________

6. friendly formulas for fyzix fun Centripetal force: F c = m v 2 / r Centripetal acceleration:a c = v 2 / r ____ Critical velocity:v min = √ r g

7. Centrifugal “force” Means “center-fleeing” If you flee from justice, you are a _______ A centrifuge does what? NOT a real force! Fake or fictitious or frame of reference “force” NO source providing an actual force NO action/reaction pair

8. Where are you “thrown”?

9. Centrifugal “force” From INSIDE the rotating frame, you FEEL pushed OUTSIDE From OUSIDE the rotating frame, you can see it is just INERTIA NO SOURCE “pushing” you out We would use this to simulate gravity in a large space station

10. Linear speed: Speed in a straight line (v) Also called “tangential speed” for an object going in a circle (still “v”) Rotational speed: number of rotations per unit of time (ω)

11. T = time period or time it takes for 1 revolution or cycle The T for a second hand on a clock would be 60 seconds Frequency: f = 1/T so the frequency for a second hand on a clock would be 1/60s or 0.017 cycles per second (called Hertz or Hz when referring to waves)

12. Remember that v = d / t Well, angular velocity is distance AROUND divided by the time it takes. This can be circumference divided by time. For example, the earth’s velocity as it revolves around the sun is the orbital circumference divided by 365 days! ( v = 2 π r / T )

13. This is sometimes measured in rpm (engines, etc.), but usually for us in radians per second. Click on motor for animation. (What’s a radian??)

15. Angular or rotational velocity ω = θ / t = ω = 1 rev / T = ω = 2 π / T = ω = 6.28 radians / T

16. So HOW are linear (tangential) velocity and angular velocity related? Q: Which U.S. state has the fastest rotational (angular) velocity? Why? Q: Which U.S. state has the fastest linear (tangential) velocity? Why? v = ω r

17. What type force is this? Which direction? What provides the source to keep the earth in orbit around the sun? Why doesn’t the earth fall into the sun? Link 1 Link Link 2

18. Which horses on the merry-go-round have the fastest rotational speed? Which horses have the fastest linear or tangential speed? (Hint: think of runners on a track)

19. LINK for example and Great connections