Displacement and arc length problems

1. Oct 17, 2012

qpzm77gg

1. v=s/t where s represents the displacement
2. s=rθ where s represents the arc length

v=rθ /t

Why can substitute here?
I guess that is not same things.

An arc length is not a straight line but displacement is which is shortest distance between initial and final point.

2. Oct 17, 2012

Philip Wood

Not quite sure I've grasped your difficulty, but for the reasoning to be valid, s in equation (1) must represent not a displacement but the arc length s. Thus v is not mean velocity over s, but speed.

3. Oct 18, 2012

qpzm77gg

Thanks. I understand now.
The equation of (1) is not velocity=displacement/time, but speed=distance/time, right?

4. Oct 18, 2012

Philip Wood

Right!

5. Oct 19, 2012

qpzm77gg

But I have some problems about it.
v=rθ /t

θ /t = angular velocity
Why speed = radius x angular velocity?
I think velocity = radius x angular velocity is suitable for it.

6. Oct 19, 2012

Philip Wood

I assume you are not treating radius and angular velocity as vectors. If you're treating them as scalars, as in most introductory courses, then the multiplication yields a scalar, which is better called speed than velocity.

In more advanced work it is possible to assign a direction to angular velocity (making it a pseudo vector), and it is clearly possible to treat instantaneous radius as a vector. By assigning a special meaning to multiplication we can produce the instantaneous velocity vector.

7. Dec 14, 2012

jpbrown1

what is the weight of a ship that displaces 500,000 kg of water?

8. Dec 14, 2012

SteamKing

Staff Emeritus
500 tonnes, more or less.