- #1

- 973

- 0

## Main Question or Discussion Point

Say I have three wheels. Their characteristics are the following:

WHEEL ONE

20 kg mass

10 cm radius

Accelerated from 0 to 10 m/s in one second

WHEEL TWO

10 kg mass

20 cm radius

Accelerated from 0 to 10 m/s in one second

WHEEL THREE

10 kg mass

10 cm radius

Accelerated from 0 to 20 m/s in one second

We assume all wheels are close enough to uniform mass density and that their moment of inertia is calculated according to (mass*radius^2), the case for a cylinder. The values above were specifically chosen so that the final angular momentum for all three wheels are the same. We now determine the rotational kinetic energy for all three wheels.

WHEEL ONE

20 kg mass

10 cm radius

Accelerated from 0 to 10 m/s in one second

Angular Momentum = 20 kg*m/s^2

Final Rotational Kinetic Energy = (1/2) * (20 kg * (10 cm)^2) * ((10 m/s)/(10 cm))^2 = 1000 Joules

WHEEL TWO

10 kg mass

20 cm radius

Accelerated from 0 to 10 m/s in one second

Angular Momentum = 20 kg*m/s^2

Final Rotational Kinetic Energy = (1/2) * (10 kg * (20 cm)^2) * ((10 m/s)/(20 cm))^2 = 500 Joules

WHEEL THREE

10 kg mass

10 cm radius

Accelerated from 0 to 20 m/s in one second

Angular Momentum = 20 kg*m/s^2

Final Rotational Kinetic Energy = (1/2) * (10 kg * (10 cm)^2) * ((20 m/s)/(10 cm))^2 = 2000 Joules

Consider that angular momentum was transferred from one wheel to the other. Apparently what I said suggests that the rotational kinetic energy does not follow a one-to-one relationship with angular momentum. What other forms of energy should be present in this scenario?

WHEEL ONE

20 kg mass

10 cm radius

Accelerated from 0 to 10 m/s in one second

WHEEL TWO

10 kg mass

20 cm radius

Accelerated from 0 to 10 m/s in one second

WHEEL THREE

10 kg mass

10 cm radius

Accelerated from 0 to 20 m/s in one second

We assume all wheels are close enough to uniform mass density and that their moment of inertia is calculated according to (mass*radius^2), the case for a cylinder. The values above were specifically chosen so that the final angular momentum for all three wheels are the same. We now determine the rotational kinetic energy for all three wheels.

WHEEL ONE

20 kg mass

10 cm radius

Accelerated from 0 to 10 m/s in one second

Angular Momentum = 20 kg*m/s^2

Final Rotational Kinetic Energy = (1/2) * (20 kg * (10 cm)^2) * ((10 m/s)/(10 cm))^2 = 1000 Joules

WHEEL TWO

10 kg mass

20 cm radius

Accelerated from 0 to 10 m/s in one second

Angular Momentum = 20 kg*m/s^2

Final Rotational Kinetic Energy = (1/2) * (10 kg * (20 cm)^2) * ((10 m/s)/(20 cm))^2 = 500 Joules

WHEEL THREE

10 kg mass

10 cm radius

Accelerated from 0 to 20 m/s in one second

Angular Momentum = 20 kg*m/s^2

Final Rotational Kinetic Energy = (1/2) * (10 kg * (10 cm)^2) * ((20 m/s)/(10 cm))^2 = 2000 Joules

Consider that angular momentum was transferred from one wheel to the other. Apparently what I said suggests that the rotational kinetic energy does not follow a one-to-one relationship with angular momentum. What other forms of energy should be present in this scenario?