# I Effects of centripetal force on longer objects

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1. Dec 29, 2017

### Physics is awesome

I have a question. What will happen if you have a long object let’s say a person was lassoed by their feet and spun around by a super strong machine or person. Since the persons head of who is being spun is moving at a much faster tangential velocity then let’s say their feet. If the rope is cut what will happen since every part of the persons body has a different tangential velocity. Will the object start spinning. Will it move in a straight line at the median tangential speed between the head and the feet? Serious question long objects are never really discussed. You can also think of the same scenario with a long piece of wood spinning around in the circle since it obviously has the same angular velocity the molecules of the wood will have a faster tangential velocity farther out. This creates a mess of what will happen in my head maybe someone could better elaborate that understands what I am asking . Thanks.

2. Dec 29, 2017

### gleem

It is easy enough to verify. Go outside and swing a long stick in a circle and let it go. It will rotate after leaving your grip. Why? Conservation of angular momentum. Which way will it rotate? Did you know it is harder to swing an extended body of mass M than an equal mass body of compact shape? What does moment of inertial have to do with this? Check out the parallel axis theorem.

3. Dec 29, 2017

### kuruman

This is a good question. Here, angular momentum is conserved because there no torques acting. Before the rope is cut, the angular momentum is $L_{before}=mvr+I_{CM}\omega$ where the first term is the angular momentum of the center of mass, $I_{CM}$ is the moment of inertia about the center of mass, $v$ is the linear speed and $\omega$ is the angular speed. Note that the object goes around the circle at the same angular speed as it spins about its center of mass ($v=\omega r$). This is exactly what happens with the Moon that shows the same face to the Earth at all times. At the moment the rope is cut, the center of mass of the extended object will move in a straight line with speed $v$ along the direction of the velocity it had just before the rope was cut. As it does so, it will continue spinning about its CM with angular speed $\omega$.

4. Dec 29, 2017