Jesus Dapena

04-18-1997, 08:39 AM

To Donald Sussman and Biomch-L:

Let's say that in the initial conditions the person and turntable

are still and the wheel is rotating counterclockwise (in a view from

overhead). That means that the combined system (person + turntable + wheel)

has counterclockwise angular momentum (all of it in the wheel). For

instance, let's say that this angular momentum is 4 Kgm2/s.

If the person then flips the wheel upside down, the wheel will now

be rotating clockwise (in a view from overhead), and therefore it will have

an angular momentum of -4 Kgm2/s (notice the negative sign, implying

clockwise rotation!) but the combined system still needs to have the same

angular momentum as before the flipping of the wheel occurred (i.e., +4

Kgm2/s). Therefore the person and the turntable will start rotating

counterclockwise with an angular momentum of +8 Kgm2/s, so that +8 Kgm2/s

(in the person+turntable) + (-4 Kgm2/s) (in the wheel) = +4 Kgm2/s in the

combined system.

All of the above assumes that the connection between the turntable

and the ground is frictionless, and therefore produces no torque about the

vertical axis.

It also assumes that the axle of the wheel is aligned with the axle

of the turntable. If not, the same basic phenomenon will still occur, but

the numbers will be somewhat different: If the axle of the wheel is

off-center relative to the axle of the turntable, the +8 Kgm2/s will be

"stored" not only in the person and in the turntable, but also partly in the

wheel itself, because it will produce the counterclockwise rotation of the

center of mass of the wheel around the vertical axis of the turntable. This

is usually called the "remote" angular momentum of the wheel (to

differentiate it from the "local" angular momentum of the wheel, which is

the -4 Kgm2/s associated with the rotation of the wheel about its own axle).

There are very good explanations of all this (and of many other

principles of rotation) in a wonderful book by Bernard Hopper: The Mechanics

of Human Movement (ISBN 0-444-19550-5). Unfortunately, the book has been

out of print for many years, but you may find it in your university library

or through inter-library loan.

Jesus Dapena

---

Jesus Dapena

Department of Kinesiology

Indiana University

Bloomington, IN 47405, USA

1-812-855-8407

dapena@valeri.hper.indiana.edu

http://www.indiana.edu/~sportbm/home.html

Let's say that in the initial conditions the person and turntable

are still and the wheel is rotating counterclockwise (in a view from

overhead). That means that the combined system (person + turntable + wheel)

has counterclockwise angular momentum (all of it in the wheel). For

instance, let's say that this angular momentum is 4 Kgm2/s.

If the person then flips the wheel upside down, the wheel will now

be rotating clockwise (in a view from overhead), and therefore it will have

an angular momentum of -4 Kgm2/s (notice the negative sign, implying

clockwise rotation!) but the combined system still needs to have the same

angular momentum as before the flipping of the wheel occurred (i.e., +4

Kgm2/s). Therefore the person and the turntable will start rotating

counterclockwise with an angular momentum of +8 Kgm2/s, so that +8 Kgm2/s

(in the person+turntable) + (-4 Kgm2/s) (in the wheel) = +4 Kgm2/s in the

combined system.

All of the above assumes that the connection between the turntable

and the ground is frictionless, and therefore produces no torque about the

vertical axis.

It also assumes that the axle of the wheel is aligned with the axle

of the turntable. If not, the same basic phenomenon will still occur, but

the numbers will be somewhat different: If the axle of the wheel is

off-center relative to the axle of the turntable, the +8 Kgm2/s will be

"stored" not only in the person and in the turntable, but also partly in the

wheel itself, because it will produce the counterclockwise rotation of the

center of mass of the wheel around the vertical axis of the turntable. This

is usually called the "remote" angular momentum of the wheel (to

differentiate it from the "local" angular momentum of the wheel, which is

the -4 Kgm2/s associated with the rotation of the wheel about its own axle).

There are very good explanations of all this (and of many other

principles of rotation) in a wonderful book by Bernard Hopper: The Mechanics

of Human Movement (ISBN 0-444-19550-5). Unfortunately, the book has been

out of print for many years, but you may find it in your university library

or through inter-library loan.

Jesus Dapena

---

Jesus Dapena

Department of Kinesiology

Indiana University

Bloomington, IN 47405, USA

1-812-855-8407

dapena@valeri.hper.indiana.edu

http://www.indiana.edu/~sportbm/home.html