Mechanics
M-R1 : Small and Large Spool
Unit
Rolling of Rigid Bodies
Purpose
Explore the relationship between rotational and translational motion in this simple but intriguing system
Equipment
Large spool with a string
Suggestions
Which way will the spool roll if
- String is pulled "over" the spool
- String is pulled "under" the spool
- Demonstrate critical angle
Discussion
- Pulling with the string over the spool
- Spool moves forward
- Pulling with string under the spool
- Spool moves forward
M-R2 : Tricycle
M-R3 : Governor
M-R4 : Flat Earth
M-R5 : Bicycle Wheel
Unit
Angular Momentum
Purpose
Illustrate conservation of angular momentum
Equipment
- Led-rim bicycle wheel with handles
- Rotating metal stool
- Electric drumell motor (20k rpm)
Suggestions
- With slow rotation of the wheel, demonstrate the effect of torque (a) turning the axis (b) breaking
- Spin fast, ask a student to (a) translate the wheeel along axis (b) turn the axle
- Ask a (small) student to sit on the stool. Hand the spinning wheel, axis vertical. Ask the student to flip the axis 180 degrees.
Discussion
M-R6 : Spinning Stool
Unit
Angular Momentum
Purpose
Illustrate conservation of angular momentum
Equipment
- Rotating metal stool
- Two hand-bars (weights)
Suggestions
- Ask a student to sit on a stool, weights in out-stretched hands
- Spin the student, and ask her to bring the weights in to her chest.
- Ask her to stretch her arms out again.
Discussion
For best results, select a student of small mass but highly developed sense of balance.
- Out-stretched arms, slower spinning rate
- Arms close to chest, faster spinning rate
M-R7 : Gyroscopes and Tops
Unit
Rotation of Rigid Body
Purpose
Illustrate conservation of angular momentum; Demonstrate precession, nutation
Equipment
- Large gyroscope听听with electric motor
- Large free gyroscope听(笔补蝉肠辞)
- Assorted other free gyroscopes
- Stand-up gyroscope听(搁耻蝉蝉颈补苍)
- Assorted tops (to be acquired)
Suggestions
- Gyroscope "remembers" a direction
- Precession changes direction when:
(a) the gravitational torque is applied at a different point
(b) direction of spinning reversed - Precession rate inversely proportional to spinning rate
Discussion
See captions from the links provided
M-R8 : Rolling Race
Unit
Rolling of Rigid Hoops, Cylinders, and Spheres
Purpose
Develop an intuition for the concept of moment of inertia and for its role in rolling motion
Equipment
- Inclined plane
- Assorted objects of rotational symmetry (cylindrical and spherical geometry)
- Two cans of soup
Suggestions
Set up races and ask for predictions of results:
- Two brass hoops; two cylinders; two spheres
- Hoop and cylinder; cylinder and sphere; hoop and sphere
- Two disks, one with a stud; sphere and spherical shell; sphere and "trick" spherical shell
- Two mystery soups (e.g. chicken broth and chicken gumbo)
Discussion
Let g be the shape factor (g=1 for cyl. shell, g=2/3 for sph. shell, g=1/2 for cylinder, g=2/5 for sphere). Then kinetic energy of rolling (without slipping) is KE=Mv2 (1+g)/2 where v is the center of mass speed. Thus objects with the smaller g win the race, independently of M.
A box with numerous objects for rolling is provided. There are also a number of "trick" objects.听
M-R9 : Balls in Grooves
Purpose
Interesting example of rolling with the variable relationship between vcm and angular velocity
Equipment
- Inclined plane with equal grooves
- Inclined plane with unequal grooves
- Metal balls of varied radiuses
Suggestions
Set up races and ask for predictions of results:
- Two identical balls, different width grooves
- Two different balls, same width grooves
- Different balls, different grooves (can achieve equal vcm!)
Discussion
Requires a careful force diagram in solving!
M-R10 : Rolling Funnel
Unit
Angular Momentum
Purpose
To demonstrate the physics of angular momentum using a funnel and ball
Equipment
- Stand with clamp
- Glass Funnel
- Clamp with ring
- Box with several small balls
Suggestions
- Let the ball roll down the funnel without circulating around the funnel's axis of symmetry
- Start the ball rolling with a circulation as nearly to the horizontal plane as possible
Discussion
For constant angular momentum, L=Iw with I=mr2, w is proportional to the inverse square of the radius of rotation
- Set-up and equipment
- Preparing to release the ball
- Spinning slowly down the funnel
- Spinning quickly down the funnel
M-R11 : Center of Gravity Paradox
Unit
Moment of Inertia
Purpose
To demonstrate r^2 dependence of moment of inertia of a point mass
Equipment
- Aluminum Rod
- Self Gripping Brass Mass
Suggestions
Poll the students for which would be the most stable postion on the rod
Discussion
The device is more stable with the mass higher up because the stabilizing moment of inertia goes up as r^2, whereas the destabilizing torque goes as r.
- Equipment
- Mass at top
- Mass at bottom
M-R12 : Flip Top
M-R13 : Foucault Pendulum
M-R14 : Hinged Stick and Falling Ball
Unit
Gravitational Acceleration
Purpose
To illustrate the difference between angular and linear acceleration
Equipment
- Hinged 39" stick with plastic cup and golf tee at unhinged end.
- Wooden Prop to seperate boards.
- One rubber and one steel ball.
Suggestions
Make sure to pull the prop out quickly trying not to disturb the board from falling straight down.
Discussion
- Equipment
- Set up
M-R15 : Lazy Susan
M-R16 : Rotational Acceleration Tank
Unit
Rotation
Purpose
Illustrate the effects of rotational motion on a fluid
Equipment
- Rotational Acceleration Tank with thumb screw and square nut (2 ea.)
- ME-8951 Rotating Platform
- ME-8955 Motor Drive (Optional)
- DC Power Supply Model: GPS-1850 (Optional)
Suggestions
- Fill the tank to about 2.5 cm.
- Use fine adjustment on the power supply for good control of angular speed.
- Use colored water e.g. cranberry juice.
Discussion
- Equipment
- Shallow parabola (low angular speed)
- Higher angular speed
- Still higher speed, parabola's vertex is below the tank
M-R17 : Rotational Cylindrical Tank
M-R18 : Spinning Balls
Unit
Angular Momentum
Purpose
Illustrate that, since, the angular momentum of the system is conserved, the ramp will speed up as the first ball rolls down the ramp, causing a delay between successive balls rolling down the ramp.
Equipment
- Rotating Platform
- Angular Momentum with three balls
- Computer Signal Interface (optional)
Suggestions
- Remember to add two counter weights when three balls are rotating.
- Try different heights for the inclined plane
- Do not rotate too fast, because balls could fly into the air
Discussion
M-R19 : Torsional Spring
Unit
Moment of Inertia
Purpose
To investigate the moment of inertia of several simple shapes, including the relationship I=f(r) for a point mass rotating about a fixed axis at a distance r.听
Equipment
- Table clamp or weighted base
- Torsion Axle
- Rod with two moveable masses
- Solid wood disk (225cm dia.)
- Solid wood cylinder (90cm dia.)
- Hollow metal cylinder (90cm dia.)
- Supporting plate for both the solid wood cylinder and hollow metal cylinder
- Circular metal disk
Suggestions
- Twist the spring so its compressed rather than stretched
- The metal disk can be rotated around several different axes
Discussion
- Equipment
- Two cylinders with equal mass, one is hollow steel and the other is solid wood
- Rod with the masses attached to it at the center
- Rod with the masses attached to it at the end
- Metal disk rotating about center of mass
- Wood disk 225cm dia