- Shows how to calculate speed required to negotiate a banked curve with friction. Derivation compares centripetal and centrifugal points of view, and can of course be used for unbanked curves and zero friction.

Artifical Gravity problem. This problem is a real thinker - once kids have a basic idea for artificial gravity. The entire problem with illustrations and the People's Physics Book can be found here (Question #22, last page).

- Shows how to calculate speed required to negotiate a banked curve with friction. Derivation compares centripetal and centrifugal points of view, and can of course be used for unbanked curves and zero friction.

Artifical Gravity problem. This problem is a real thinker - once kids have a basic idea for artificial gravity. The entire problem with illustrations and the People's Physics Book can be found here (Question #22, last page).

A space station was established far from the gravitational field of Earth. Extended stays in zero gravity are not healthy for human beings. Thus, for the comfort of the astronauts, the station is rotated so that the astronauts feel there is an internal gravity. The rotation speed is such that the apparent acceleration of gravity is 9.8 m/s2. The direction of rotation is counter-clockwise. a. If the radius of the station is 80 m, what is its rotational speed, v? b. Draw vectors representing the astronaut’s velocity and acceleration. c. Draw a free body diagram for the astronaut. d. Is the astronaut exerting a force on the space station? If so, calculate its magnitude. Her mass m = 65 kg. e. The astronaut drops a ball, which appears to accelerate to the ‘floor’, (see picture) at 9.8 m/s2. i. Draw the velocity and acceleration vectors for the ball while it is in the air. ii. What force(s) are acting on the ball while it is in the air? iii. Draw the acceleration and velocity vectors after the ball hits the floor and comes to rest. iv. What force(s) act on the ball after it hits the ground? Contributed by Bill Taylor

Center-directed Forces materials produced by ASU's Modeling Physics are available through the American Modeling Teachers Association's membership website. The link above is to the Mechanics portion. Membership is required to access these materials.

Centripetal Force on an Airplane - Thanks Joe Stieve. These airplanes are available from physicstoolbox.com. Students love this one but it requires a little more maturity.

Virtual lab using Direct Measurement Videos: Students use conservation of energy to determine the expected velocity of two different falling/rotating objects: a disk and a hoop. They then analyze videos to determine the experimental value of velocity and calculate percent error. A third, irregular object (bicycle wheel with spokes and hub) is then analyzed to determine the coefficient of mr^2 for this arrangement of mass. Students continue to a conservation of angular momentum analysis.

Students determine the minimum tensile strength required for a leash to be used on flying pigs. Students also find net radial F (aka centripetal), net radial acceleration, tangential velocity, angular speed and so on.

Flying Pig Canonical Pendulum 1. Author: Bill Taylor, //bt4_1284@yahoo.com// 2. A toy flying pig is a canonical pendulum. By measuring the mass of the pig and the radius of the pendulum, one can determine the (theoretical) equilibrium speed of the pig. This can be compared to the actual speed. I use this Lab in AP-C, but it could also be used in an Honors course.

Flying Pig Conical Pendulum Lab My version of this popular lab. You will see that there are no direction for students on how to measure the radius of the circle the pig flies in. That is the fun part. They will come up with several methods that work, hopefully before the pig hits them in the head a few times. Dan Burns version of Paul Robinson's lab.

Flying Pig Conical Pendulum with an AP Twist I took Martha Leitz's conical pendulum lab and melded it with "The Helicopter Ride" from Practicums for Physics Teachers by Henry Ryan and Jon Barber to create this small group lab. Works great- and very helpful since my 2nd year students have already seen the traditional lab. Author: Jen Grady (jgrady@hononegah.org)

1. Author: Ralph von Philp, vonphilp@myactv.net 2. This is a blend of some of the other labs on this page involving a flying pig or airplane and circular motion.

David Green's Circular Motion Apparatus. Note long Download 15 Meg

Allows one to calculate the moment of inertia of the platform and object using Pasco's Rotary Motion Sensor. You can use the included metal ring or rod with adjustable weights, or for added fun, try building a cage out of balsa wood, glue it to the platform, and find the moment of inertia of a (hard-boiled) egg. I don't have a full lab procedure at the moment, but I use masses between 10 - 60 g and the smallest radius setting on the spindle.

Circular Motion Example Problem Powerpoint Slides I used these to create screencasts that I post on Youtube for my students. They are meant for students that miss class or want to see additional examples. Some are follow-up examples to labs and demos done in class. You could use them to show in class or to create your own screencasts with your own voice for your students to hear. Video and audio files need to be downloaded separately and re-inserted into the slideshow. Feel free to modify them as you wish. Attribution to me is not necessary but please send me any errors you notice or other comments that might improve them. Dan Burns (dburns@lgsuhsd.org)

Rotor Lab - A lab using a turntable to create an amusement park ride called The Rotor. It is a free response question on the 1984 Mechanics C test and a sample problem in Halliday Resnick and Walker chapter 9, deleted from 9th edition :( See The Rotor ppt above for more info on this. The Rotor is a cylinder that spins on a vertical axis. Riders stand against the wall which pushes in on them. The floor drops but they stay in place because of static friction. This would work well as a demo lab if you only have one turntable. I have developed a Lazy Susan Rotor that works well and is very inexpensive, see the pdf file below for pictures and details. The vesion of the lab I use uses angular velocity. If you want one using linear velociyt, see the "noOmega" version. See the lab, video and stills below - Dan Burns

Angular Speed Lab - Introductory activity where class gets in a line and spins at a constant angular speed. They calculate their own linear and angular speed and answer some questions related to angular speed. If you can't find room to do this or the weather is bad, consider having them watch the video link below and do the same for one of the skaters. It is an attempt to set the world record for spinning in a line on ice. There are 70 skaters and I estimate they have a period of 16 s. Assuming 0.5 m/skater, this is a linear speed of 6.9 m/s for the outside skater. - Dan Burns

Moved by Robert...## There are also activities posted in the Newton's Laws section that involve circular motion.

NOTES and DERIVATIONS: below

Circular Motion & Universal Gravitation. Notes from Wayne Mullins. Wayne's (now somewhat old) notes can be accessed at

https://mus.haikulearning.com/wayne.mullins/apphysics1201516/cms_page/view/19696981

Centripetal/Centrifugal Force on a banked curve -

Artifical Gravity problem. This problem is a real thinker - once kids have a basic idea for artificial gravity. The entire problem with illustrations and the People's Physics Book can be found here (Question #22, last page).

Centripetal/Centrifugal Force on a banked curve -

Artifical Gravity problem. This problem is a real thinker - once kids have a basic idea for artificial gravity. The entire problem with illustrations and the People's Physics Book can be found here (Question #22, last page).

A space station was established far from the gravitational field of Earth. Extended stays in zero gravity are not healthy for human beings. Thus, for the comfort of the astronauts, the station is rotated so that the astronauts feel there is an internal gravity. The rotation speed is such that the apparent acceleration of gravity is 9.8 m/s2. The direction of rotation is counter-clockwise.

a. If the radius of the station is 80 m, what is its rotational speed, v?

b. Draw vectors representing the astronaut’s velocity and acceleration.

c. Draw a free body diagram for the astronaut.

d. Is the astronaut exerting a force on the space station? If so, calculate its magnitude. Her mass m = 65 kg.

e. The astronaut drops a ball, which appears to accelerate to the ‘floor’, (see picture) at 9.8 m/s2.

i. Draw the velocity and acceleration vectors for the ball while it is in the air.

ii. What force(s) are acting on the ball while it is in the air?

iii. Draw the acceleration and velocity vectors after the ball hits the floor and comes to rest.

iv. What force(s) act on the ball after it hits the ground?

Contributed by Bill Taylor

LABS & APPRATUS below

Central Force Model:

Centripetal Force on an Airplane - Thanks Joe Stieve. These airplanes are available from physicstoolbox.com. Students love this one but it requires a little more maturity.

Web Resources in Forces, equilibrium and more (by the College Board).

Rotational Kinetic Energy and Angular Momentum Using Direct Measurement Videos

Flying Pig Centripetal Force farming-flying-pigs.doc

Flying Pig Canonical Pendulum

1. Author: Bill Taylor, //bt4_1284@yahoo.com//

2. A toy flying pig is a canonical pendulum. By measuring the mass of the pig and the radius of the pendulum, one can determine the (theoretical) equilibrium speed of the pig. This can be compared to the actual speed. I use this Lab in AP-C, but it could also be used in an Honors course.

Flying Pig Conical Pendulum Lab

My version of this popular lab. You will see that there are no direction for students on how to measure the radius of the circle the pig flies in. That is the fun part. They will come up with several methods that work, hopefully before the pig hits them in the head a few times. Dan Burns version of Paul Robinson's lab.

Flying Pig Conical Pendulum with an AP Twist

I took Martha Leitz's conical pendulum lab and melded it with "The Helicopter Ride" from Practicums for Physics Teachers by Henry Ryan and Jon Barber to create this small group lab. Works great- and very helpful since my 2nd year students have already seen the traditional lab. Author: Jen Grady (jgrady@hononegah.org)

Flying In Circles

1. Author: Ralph von Philp, vonphilp@myactv.net

2. This is a blend of some of the other labs on this page involving a flying pig or airplane and circular motion.

David Green's Circular Motion Apparatus. Note long Download 15 Meg

## Link to Rotational Energy lab

Pasco Rotary Motion Sensor Rotational Apparatus.pdf

Circular Motion Example Problem Powerpoint Slides I used these to create screencasts that I post on Youtube for my students. They are meant for students that miss class or want to see additional examples. Some are follow-up examples to labs and demos done in class. You could use them to show in class or to create your own screencasts with your own voice for your students to hear. Video and audio files need to be downloaded separately and re-inserted into the slideshow. Feel free to modify them as you wish. Attribution to me is not necessary but please send me any errors you notice or other comments that might improve them. Dan Burns (dburns@lgsuhsd.org)

Rotor Lab - A lab using a turntable to create an amusement park ride called The Rotor. It is a free response question on the 1984 Mechanics C test and a sample problem in Halliday Resnick and Walker chapter 9, deleted from 9th edition :( See The Rotor ppt above for more info on this. The Rotor is a cylinder that spins on a vertical axis. Riders stand against the wall which pushes in on them. The floor drops but they stay in place because of static friction. This would work well as a demo lab if you only have one turntable. I have developed a Lazy Susan Rotor that works well and is very inexpensive, see the pdf file below for pictures and details. The vesion of the lab I use uses angular velocity. If you want one using linear velociyt, see the "noOmega" version. See the lab, video and stills below - Dan Burns

Angular Speed Lab - Introductory activity where class gets in a line and spins at a constant angular speed. They calculate their own linear and angular speed and answer some questions related to angular speed. If you can't find room to do this or the weather is bad, consider having them watch the video link below and do the same for one of the skaters. It is an attempt to set the world record for spinning in a line on ice. There are 70 skaters and I estimate they have a period of 16 s. Assuming 0.5 m/skater, this is a linear speed of 6.9 m/s for the outside skater. - Dan Burns

https://youtu.be/gvxTMFBzbFc