Understanding Stopping Distance & Its Relation to Speed and Angular Movement

[Sundown444]

As I have heard, for a moving object, stopping distance is proportional to the square of the speed. Is this true, and does this apply to angular movements such as body part movements?

 

[jbriggs444]

As I have heard, for a moving object, stopping distance is proportional to the square of the speed. Is this true, and does this apply to angular movements such as body part movements?

Yes, given a fixed deceleration rate, stopping distance is proportional to the square of the starting speed. It makes sense that this should be so. It takes twice as long to slow down and during the slowdown interval, it is moving twice as fast.

Yes, for a fixed angular deceleration rate, the angle traversed during the slowdown is proportional to the square of the starting rotation rate. The same reasoning applies.

Of course, the deceleration rate is not always going to be equal. No matter how fast you swing your fist, it will usually stay attached to the end of your arm. Your muscles, tendons and ligaments will apply whatever force they are able to preserve that situation. Swinging twice as fast will not work to strike a fellow standing on the opposite side of the boxing ring.

 

[Sundown444]

Yes, given a fixed deceleration rate, stopping distance is proportional to the square of the starting speed. It makes sense that this should be so. It takes twice as long to slow down and during the slowdown interval, it is moving twice as fast.

Yes, for a fixed angular deceleration rate, the angle traversed during the slowdown is proportional to the square of the starting rotation rate. The same reasoning applies.

Of course, the deceleration rate is not always going to be equal. No matter how fast you swing your fist, it will usually stay attached to the end of your arm. Your muscles, tendons and ligaments will apply whatever force they are able to preserve that situation. Swinging twice as fast will not work to strike a fellow standing on the opposite side of the boxing ring.

So, stopping distance applies to swinging your arms in a circular fashion at some speed as well?

 

[jbriggs444]

So, stopping distance applies to swinging your arms in a circular fashion at some speed as well?

Yes. Like a woman's softball pitcher?

 

[Sundown444]

Yes. Like a woman's softball pitcher?

Yes, something like that.

 

[sophiecentaur]

Yes. Like a woman's softball pitcher?

You could be in trouble with the sexism police with that remark. But I know what you mean about male and female throwing methods. Bowling, both in Women's and Mens' cricket involves the same action (100mph+).

stopping distance is proportional to the square of the speed.

Yes, the Kinetic Energy is mv²/2 and the distance taken will be, in simple terms , proportional to the distance because Work (energy dissipated by brakes) is Brake Force times distance. For a constant braking force, this means distance is proportional to v².
For rotation, the same thing applies; number of revolutions to stop will depend on rotation speed squared.
But bodies are not good subjects to try to do basic Physics with. Far too complicated for simple sums. (Same with car collisions)

 

[Sundown444]

So, one other thing: does stopping distance apply to anything, including projectiles?

 

[jbriggs444]

So, one other thing: does stopping distance apply to anything, including projectiles?

What does this question mean? If something is moving over here and comes to a stop over there, you can take the distance between here and there as the stopping distance. In this sense, "stopping distance" applies to anything, including projectiles.

If you mean to ask whether stopping distance always goes as the square of starting velocity, the answer is no. The stopping force (and how that force varies over time) matters too.

 

[Sundown444]

What does this question mean? If something is moving over here and comes to a stop over there, you can take the distance between here and there as the stopping distance. In this sense, "stopping distance" applies to anything, including projectiles.

If you mean to ask whether stopping distance always goes as the square of starting velocity, the answer is no. The stopping force (and how that force varies over time) matters too.

So what do you mean by stopping force? What can it be?

 

[Nugatory]

So what do you mean by stopping force? What can it be?

The stopping force is whatever force is acting on the object to slow it down. Throw an object up into the air and gravity will eventually stop it; brake a car and the force between the tires and the road will eventually stop it; throw a ball into a net and the force of the net on the ball will stop it (and in this last example the stopping distance probably is not proportional to the square of the speed).

If there isn't some force acting to slow and stop the object it will keep on moving forever, according to Newton's first law.