# 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.