# Understanding constant velocity, inertia and rest

## Main Question or Discussion Point

I've come to the conclusion that i don't understand at all the concept behind inertia. How can we know when an object stays at rest or at constant velocity? (take for example a girl in a rope. She would tighten her grip on the rope until the tension balances the force of gravity (assume rope is frictionless). This means that she would then have no net force acting on her. Does she stop or does she continue at constant velocity? Why is this for any answer?)

On the other hand, if we have a rocket and we drop from say, an airplane (this airplane is going at constant velocity). When the rocket starts to fall in free-fall (ignore all other forces) does the rocket continue with a horizontal velocity of zero or does go at the same horizontal velocity of the plane? For any of the answers, why is this? (and also, if we make a generalization to most cases)

Thank you very much for your patience.

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Doc Al
Mentor
I've come to the conclusion that i don't understand at all the concept behind inertia. How can we know when an object stays at rest or at constant velocity? (take for example a girl in a rope. She would tighten her grip on the rope until the tension balances the force of gravity (assume rope is frictionless). This means that she would then have no net force acting on her. Does she stop or does she continue at constant velocity? Why is this for any answer?)
If the net force on her is zero, the girl's acceleration is zero. So she will continue to move with a constant velocity. If she's at rest, she will remain at rest; if moving, she will remain moving.

If the girl is sliding down a rope and wants to stop her descent, then she'll have to grip the rope tight enough so that the tension is greater than gravity. (And the rope better have friction, else all her gripping won't help.)

On the other hand, if we have a rocket and we drop from say, an airplane (this airplane is going at constant velocity). When the rocket starts to fall in free-fall (ignore all other forces) does the rocket continue with a horizontal velocity of zero or does go at the same horizontal velocity of the plane? For any of the answers, why is this? (and also, if we make a generalization to most cases)
If you drop something from an airplane, then that something is already moving with the same horizontal velocity as the airplane. So it will continue to do so unless something exerts a force to change that.

A.T.
On the other hand, if we have a rocket and we drop from say, an airplane (this airplane is going at constant velocity). When the rocket starts to fall in free-fall (ignore all other forces) does the rocket continue with a horizontal velocity of zero or does go at the same horizontal velocity of the plane?

At 0.08 you see low drag bombs, with negligible air resistance. Later retarded bombs.

So then the objects continue moving at the same velocity (if it's constant). However, if one is accelerating, then we would see that one of them actually is "falling behind"? (if another force acted on the bombs as they fall)

As an example, if we have a toy cart with a cannon and we fire a cannonball (this toy cart is moving at constant velocity), then would the ball return at the exact position where the cannon is? And if the cart is accelerating (say speeding up), then would the ball fall behind the cannon?

On the other hand, whenever an object is accelerating and suddenly its net force drops to 0, then it would continue moving at constant velocity? (if the objects move and the net force turns to zero, then would the objects be at rest or moving? What's the distinction?)

A.T.
What's the distinction?
There is no physically significant distinction between rest and constant velocity. Just a matter of coordiantes used to describe the movement.

Doc Al
Mentor
As an example, if we have a toy cart with a cannon and we fire a cannonball (this toy cart is moving at constant velocity), then would the ball return at the exact position where the cannon is? And if the cart is accelerating (say speeding up), then would the ball fall behind the cannon?
If you fire the cannon ball straight up, yes.

On the other hand, whenever an object is accelerating and suddenly its net force drops to 0, then it would continue moving at constant velocity?
Right.

(if the objects move and the net force turns to zero, then would the objects be at rest or moving? What's the distinction?)
Why would the objects be at rest? If they were moving when the net force went to zero, they would remain moving.

As A.T. says, there's nothing special about rest versus moving at constant velocity. Zero is a perfectly legitimate velocity! (Whether something is at rest just depends on the reference frame used.)

If you fire the cannon ball straight up, yes.

Right.

Why would the objects be at rest? If they were moving when the net force went to zero, they would remain moving.

As A.T. says, there's nothing special about rest versus moving at constant velocity. Zero is a perfectly legitimate velocity! (Whether something is at rest just depends on the reference frame used.)
Yep, i was talking about a straight up cannon.

So we can consider "rest" as being a special case of constant velocity (in which it is zero). So this would only depend on the conditions of the problem? (if it isn't stated, and the object was moving, by having a net force of zero, can i assume the object is at rest?)

I think i'm getting it right now. Thank you!

Doc Al
Mentor
So we can consider "rest" as being a special case of constant velocity (in which it is zero).
Sure.

So this would only depend on the conditions of the problem?
It should be clear from the context of the problem whether the system in question is moving or stationary. (Sometimes it doesn't matter.)

(if it isn't stated, and the object was moving, by having a net force of zero, can i assume the object is at rest?)
You might want to rephrase that question.