# Homework Help: Why does an object have constant speed with Centripetal Force

1. Jan 26, 2010

### Masafi

Hi, I understand how centripetal force works and all. But I still don't understand, when looking at a satellite orbiting the Earth, the only force acting is its weight, which is in the direction of the Earth.

How does its circular motion start in the first place? If the only force there is is acting towards the Earth, why doesn't it just move towards the Earth? Surely something must happen to get the circular spin to begin, like with a hammer thrower, they spin it physically to begin the motion.

Why does a fixed distance remain from the Earth? And also, why does its speed not change at all?

2. Jan 26, 2010

### fluidistic

In the case of the circular motion of a satellite, the weight of the satellite is also its centripetal force. In a circular motion with constant speed, the only force applied on the body is precisely the centripetal force, so all is coherent.

Why does the satellite does not fall over the Earth if the only force is toward the center of the Earth? Because as you said, something made it start to move in a circular motion. The original impulse has to be applied perpendicularly to the centripetal force. If it has enough impulse, the motion will be circular. If it has a too tiny impulse it will eventually fall over the Earth. If it has an impulse bigger than the one required for the circular motion, I think the motion will be elliptic, but I'm not 100% sure.

The speed is the magnitude of the velocity. In a circular motion, $$a_c=\frac{v^2}{r}$$. In the case of the satellite, $$a_c$$ ( and r) is constant, making that v (the speed, and not velocity) must be constant.

I'll let others to explain it better than I. Do you still have doubts?

3. Jan 26, 2010

### Masafi

Well, why does the magnitude of the velocity, i.e. the speed, remain constant? Why doesn't it accelerate closer towards the Earth?

If something has a force, say a person dragging something, why does that go towards the person, whilst in a circular motion, it spins around?

4. Jan 26, 2010

### DaveC426913

Well, it does. But its tangential velocity carries it past Earth. An orbiting body could be viewed as a falling body that keeps missing its target.

5. Jan 26, 2010

### Masafi

And why doesn't it hit the target? Why is there a tangential acting velocity?

6. Jan 26, 2010

### DaveC426913

The object was initially imbued with it.