Displacement and arc length problems

[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.

 

[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.

 

[qpzm77gg]

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.

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

 

[Philip Wood]

Right!

 

[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.

 

[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.

 

[jpbrown1]

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

 

[SteamKing]

500 tonnes, more or less.