Question about circular motion

[Metal Mario]

This is technically homework, but not for a grade, since this isn't for a class. This is purely so I can learn for personal interest.

I'm reading a basic physics book. I am at the part where it's talking about circular motion. One example question in it asks: If you attached a string to a rock, and whirled it around in a circle, then the string broke (let's say in a counter-clockwise direction, and the string broke at the number 3), what direction would the rock go? The possibilities are: straight out from the 3, or it would continue moving in a straight line upward if seen from an overhead view.

Well, I've done that a lot, and when I release something, it always goes straight out, so I chose straight out. But it says the correct answer is it will continue moving upward (if seen from above, it would appear to be up) and perpendicular to a line from the point the string broke to the center of the circle, so it would appear to be going straight up from the number 3 on a flat clock.

My question is why? When I twirl something around and let go of it, it flies straight out and away from me in a straight line. My idea is that momentum is carrying the object away in a straight line, but that the string is keeping it an equal distance away from me at every point along the circle, until the string no longer holds it, and that as long as the string is holding it, it is moving in a circular motion.

Can someone please explain why the book says the correct answer is that (if viewed from above, looking down at the flat 2D plane) the rock would appear to go up in a straight line from the number 3 where the string broke (assuming a counter-clockwise motion)?

[WarSun]

While constantly circling around a center, the rock will always have two vectors acting on it (forces in two direction).

1. towards the center

2. at tangent or perpendicular to the string

The direction of these two forces keep changing as the rock travels along the circular path. Taking these two forces into account, the final or resultant force would be along the circumference of the circle. In your case, when the string is cut, the force acting towards the center is removed and the only force acting on the rock would be the force that is perpendicular to the string, ( which is upward if seen from above ). 

Another example would be- if the sun's gravitational pull suddenly disappears, then earth would continuously keep moving towards the tangent direction of its orbit.   

[studiot]

25 minutes ago, Metal Mario said:

When I twirl something around and let go of it

Think carefully about how you are doing this.

It is pretty well impossible to keep you hand in the centre of the circle with a string.
I expect your hand is actually describing its own circular motion, not rotating about a point.

This imparts sideways motion as well as circular.

Twirling in a vertical plane as you describe also make it more difficult.

 

Have a go with a very heavy weight and a more nearly horizontal circle, or watch the hammer throw in athletics.

Which way does it go?

[Metal Mario]

Ok, after watching that carefully, it looked like the ball flew in a direction 90 degrees from the line beginning with the center (the guy) and extending to the point it was released. Maybe when I flung things like this, it was happening so fast that I thought I released it in line with its destination, but really released it at a perpendicular direction from the center to the point it was released. I now see your point.

But now that brings up a different question. When things get pushed toward the interior perimeter of a hollow round container as it spins around, is the reason for that not because the objects are pushing directly out from the center as I thought, but because of the path they want to go, which is extending in a perpendicular direction from their instantaneous position on the perimeter of the circle, which pushes them outward toward the perimeter of the circle because their "desired" path would be to take them outside the circle? I hope I worded that in a way that can be understood.

[swansont]

4 hours ago, Metal Mario said:

My question is why? When I twirl something around and let go of it, it flies straight out and away from me in a straight line. My idea is that momentum is carrying the object away in a straight line, but that the string is keeping it an equal distance away from me at every point along the circle, until the string no longer holds it, and that as long as the string is holding it, it is moving in a circular motion.

What does Newton's first law tell you?

[Metal Mario]

Thanks for taking time to help guys. It makes sense to me now.

[muskan]

the velocity in circular motion is prependicular to path. that's why, if you release the stone, it will move in the direction of the tangent at that point.