KhashayarShatti

2012-Jan-03, 11:47 AM

I honestly don't know if this is ATM. I think of it as a simple engineering problem.

My question is: Is the weight of a rotating object equal to its stationary weight?

For simplicity please consider a rotating ring of radius r, Gravitational constant G, speed of w1 vertically downwards(horizontal ring plane), ring cross section to be very small.

I've done some calculations as follows and i've come to the conclusion that the weight is less. Experimentally i don't have an accurate weighing set, so my argument is mathematical as follows:

1- Consider any particle on the ring with a mass of m,

2- Radius of earth=R metres.

3- Speed about its own axis=w1 rad/s vertically downwards.

4- Radius of spin=r metres

5- So the tangential speed of the particle=r*w1

6- Now this particle is moving in the gravity field of earth and this gravity force causes it to experience a curved path if it was allowed to by the ring . For this reason i've taken w2 as the speed of this particle around earth at that moment. w2 axis will be horizontal.

7- Now if an object spins and is given a torque to rotate(caused by gravity) then a third speed w3 will be induced on the particle by the formula T=I*w1*w2 . This torque induces w3. Direction of w3 is also horizontal and at righe angles to w2 and w1.

8- This torque induces an upward force on the particle=T/r.

9- So the actual weight of the object=mg-T/r.

All my question is on item no. 6. Is this correct? If not, why not?

My question is: Is the weight of a rotating object equal to its stationary weight?

For simplicity please consider a rotating ring of radius r, Gravitational constant G, speed of w1 vertically downwards(horizontal ring plane), ring cross section to be very small.

I've done some calculations as follows and i've come to the conclusion that the weight is less. Experimentally i don't have an accurate weighing set, so my argument is mathematical as follows:

1- Consider any particle on the ring with a mass of m,

2- Radius of earth=R metres.

3- Speed about its own axis=w1 rad/s vertically downwards.

4- Radius of spin=r metres

5- So the tangential speed of the particle=r*w1

6- Now this particle is moving in the gravity field of earth and this gravity force causes it to experience a curved path if it was allowed to by the ring . For this reason i've taken w2 as the speed of this particle around earth at that moment. w2 axis will be horizontal.

7- Now if an object spins and is given a torque to rotate(caused by gravity) then a third speed w3 will be induced on the particle by the formula T=I*w1*w2 . This torque induces w3. Direction of w3 is also horizontal and at righe angles to w2 and w1.

8- This torque induces an upward force on the particle=T/r.

9- So the actual weight of the object=mg-T/r.

All my question is on item no. 6. Is this correct? If not, why not?