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

  1. String is pulled "over" the spool
  2. String is pulled "under" the spool
  3. Demonstrate critical angle

Discussion

  1. Pulling with the string over the spool
  2. Spool moves forward
  3. Pulling with string under the spool
  4. Spool moves forward

M-R2 : Tricycle

Unit

Rolling of Rigid Bodies

Purpose

See comments for large and small spools

Equipment

  1. Tricycle
  2. Rope

Suggestions

Discussion

M-R3 : Governor

Unit

Rotational Dynamics

Purpose

Illustrates the role of centripetal force

Equipment

  1. Variable speed drill
  2. Governor assembly

Suggestions

Discussions

1. Set-up

2-4. The position of the governor's masses as the rotational speed is gradually increased

M-R4 : Flat Earth

Unit

Rotational Dynamics

Purpose

Illustrates the role of cenripetal of force

Equipment

  1. Variable speed drill
  2. Flattening device

Suggestions

Discussions

1. Set-up

2-3. The shape of the device as the rotational speed is gradually increased

M-R5 : Bicycle Wheel

Unit

Angular Momentum

Purpose

Illustrate conservation of angular momentum

Equipment

  1. Led-rim bicycle wheel with handles
  2. Rotating metal stool
  3. Electric drumell motor (20k rpm)

Suggestions

  1. With slow rotation of the wheel, demonstrate the effect of torque (a) turning the axis (b) breaking
  2. Spin fast, ask a student to (a) translate the wheeel along axis (b) turn the axle
  3. 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

  1. Rotating metal stool
  2. Two hand-bars (weights)

Suggestions

  1. Ask a student to sit on a stool, weights in out-stretched hands
  2. Spin the student, and ask her to bring the weights in to her chest.
  3. Ask her to stretch her arms out again.

Discussion

For best results, select a student of small mass but highly developed sense of balance.

  1. Out-stretched arms, slower spinning rate
  2. 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

  1. Large gyroscope听听with electric motor
  2. Large free gyroscope听(笔补蝉肠辞)
  3. Assorted other free gyroscopes
  4. Stand-up gyroscope听(搁耻蝉蝉颈补苍)
  5. Assorted tops (to be acquired)

Suggestions

  1. Gyroscope "remembers" a direction
  2. Precession changes direction when:
    (a) the gravitational torque is applied at a different point
    (b) direction of spinning reversed
  3. 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

  1. Inclined plane
  2. Assorted objects of rotational symmetry (cylindrical and spherical geometry)
  3. Two cans of soup

Suggestions

Set up races and ask for predictions of results:

  1. Two brass hoops; two cylinders; two spheres
  2. Hoop and cylinder; cylinder and sphere; hoop and sphere
  3. Two disks, one with a stud; sphere and spherical shell; sphere and "trick" spherical shell
  4. 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

  1. Inclined plane with equal grooves
  2. Inclined plane with unequal grooves
  3. Metal balls of varied radiuses

Suggestions

Set up races and ask for predictions of results:

  1. Two identical balls, different width grooves
  2. Two different balls, same width grooves
  3. 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

  1. Stand with clamp
  2. Glass Funnel
  3. Clamp with ring
  4. Box with several small balls

Suggestions

  1. Let the ball roll down the funnel without circulating around the funnel's axis of symmetry
  2. 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

  1. Set-up and equipment
  2. Preparing to release the ball
  3. Spinning slowly down the funnel
  4. 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

  1. Aluminum Rod
  2. 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.

  1. Equipment
  2. Mass at top
  3. Mass at bottom

Manual Pages:听(1)听(2)听(3)听(4)听(5)

M-R12 : Flip Top

Unit

Rotation

Purpose

Rotational Dynamics

Equipmemt

  1. Wooden Top
  2. Small Shoe Lace
  3. Handle

Suggestions

Put the top into the side hole on the handle, then thread the shoe lace in and wind it around the top.

Discussion

  1. Equipment
  2. Getting the top spinning
  3. Top spinning
  4. Top flipped over

M-R13 : Foucault Pendulum

Unit

Inertia (Pendulum)

Purpose

To demonstrate how a Foucault pendulum works

Equipment

Cenco Projectual Foucault Pendulum

Suggestions

  1. Gently rotate the platform while the pendulum swings
  2. Do not use to demonstrate Coriollis Effect

Discussion

  1. Pendulum over the North Pole
  2. Pendulum Swinging
  3. Overhead

Manual Pages:(1)听(2)听(3)听(4)听(5)听(6)听(7)听(8)听(9)听(10)听听

M-R14 : Hinged Stick and Falling Ball

Unit

Gravitational Acceleration

Purpose

To illustrate the difference between angular and linear acceleration

Equipment

  1. Hinged 39" stick with plastic cup and golf tee at unhinged end.
  2. Wooden Prop to seperate boards.
  3. 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

  1. Equipment
  2. Set up

Manual Page:(1)听(2)听(3)听(4)听听

M-R15 : Lazy Susan

Purpose

To explore rotating objects

Equipment

  1. Lazy Susan Rotational Platform

Suggestions

  1. Take caution when standing on the platform
  2. Use with dumbbells to show moment of inertia

Discussion

M-R16 : Rotational Acceleration Tank

Unit

Rotation

Purpose

Illustrate the effects of rotational motion on a fluid

Equipment

  1. Rotational Acceleration Tank with thumb screw and square nut (2 ea.)
  2. ME-8951 Rotating Platform
  3. ME-8955 Motor Drive (Optional)
  4. DC Power Supply Model: GPS-1850 (Optional)

Suggestions

  1. Fill the tank to about 2.5 cm.
  2. Use fine adjustment on the power supply for good control of angular speed.
  3. Use colored water e.g. cranberry juice.

Discussion

  1. Equipment
  2. Shallow parabola (low angular speed)
  3. Higher angular speed
  4. Still higher speed, parabola's vertex is below the tank

M-R17 : Rotational Cylindrical Tank

Unit

Rotating Fluids

Purpose

Illustrate rotating fluid in a circular container

Equipment

  1. Cran-Grape Juice
  2. Clear Cylindrical Tank
  3. Rotating Platform
  4. A power supply connected to the Motor
  5. Styrofoam Braces

Suggestions

See suggestions for rectangular rotating tank

Discussion

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

  1. Rotating Platform
  2. Angular Momentum with three balls
  3. Computer Signal Interface (optional)

Suggestions

  1. Remember to add two counter weights when three balls are rotating.
  2. Try different heights for the inclined plane
  3. 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

  1. Table clamp or weighted base
  2. Torsion Axle
  3. Rod with two moveable masses
  4. Solid wood disk (225cm dia.)
  5. Solid wood cylinder (90cm dia.)
  6. Hollow metal cylinder (90cm dia.)
  7. Supporting plate for both the solid wood cylinder and hollow metal cylinder
  8. Circular metal disk

Suggestions

  1. Twist the spring so its compressed rather than stretched
  2. The metal disk can be rotated around several different axes

Discussion

  1. Equipment
  2. Two cylinders with equal mass, one is hollow steel and the other is solid wood
  3. Rod with the masses attached to it at the center
  4. Rod with the masses attached to it at the end
  5. Metal disk rotating about center of mass
  6. Wood disk 225cm dia

Manual Page:(1)听(2)听(3)听(4)听(5)听听

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