Different conversion for angular momentum

[negation]

Homework Statement

Express the units of angular momentum (a) using only the fundamental units kilogram, meter, and second; (b) in a form involving Newtons; (c) in a form involving joules.

The Attempt at a Solution

a) L = r x p = r x mv = Iω

This can be simplified to kgm²/s

b) L = r x p = r x mv
I express r in meter m , m in kg and v in ms^-1

what I got was m²kg/s

I have to convert it to n.m.s

 

[Chestermiller]

What are the fundamental units of a Newton? What are the fundamental units of a Joule?

Chet

 

[negation]

What are the fundamental units of a Newton? What are the fundamental units of a Joule?

Chet

Hi!

1N is equivalent to the force required to give a mass of 1kg an acceleration of 1m/^2.
1kg.m.s^-2

1J is the work done by applying a force of 1N over a meter.

 

[Chestermiller]

Hi!

1N is equivalent to the force required to give a mass of 1kg an acceleration of 1m/^2.
1kg.m.s^-2

1J is the work done by applying a force of 1N over a meter.

So, again, what are the units?

 

[negation]

So, again, what are the units?

They are kg.m.s^-1 and kg.m².s^-2

 

[Chestermiller]

They are kg.m.s^-1 and kg.m².s^-2

For Newtons, that should be kg.m.s^-2. Now the trick is combine these with your units for angular momentum to express the angular momentum in terms of N, m, and sec, or J, m, and sec.

Chet

 

[negation]

For Newtons, that should be kg.m.s^-2. Now the trick is combine these with your units for angular momentum to express the angular momentum in terms of N, m, and sec, or J, m, and sec.

Chet

Let me give the brick wall another shot.

 

[negation]

Still finding it very difficult to solve. Any hints?

 

[Chestermiller]

Still finding it very difficult to solve. Any hints?

Solve for kg in one set of units, and substitute for it into the other set of units.

Chet

 

[negation]

Solve for kg in one set of units, and substitute for it into the other set of units.

Chet

Thanks Chet.

L = m²kg.s^-1

1N = 1kg ms^-2

∴1kg = 1Ns²/m

In subtituing into L:

m²(1Ns²/m) s^-1

=n.m.s

1J = 1Js²/m²

In substituting into L:

∴ m²(1Js²/m²)s^-1
= 1J.s

Both are consistent with the system's answer.

It has also enabled me to solve a next different question that asked for J.s.