# 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 with electric motor
- Large free gyroscope (Pasco)
- Assorted other free gyroscopes
- Stand-up gyroscope (Russian)
- 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.

## 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=mr^{2}, 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.

### 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