# Does a horizontally spinning weight = no motion weight?

1. Aug 2, 2012

### evowerks

Imagine a person weighing 99kg stands on a bathroom scale. He reads 99kg. That same person then grabs a ball attached to a string that weighs 1kg together. Since he never left the scale he now reads 100kg total.
Now imagine he spins the ball and string like a helicopter overhead. (Since hes a big dude he can do this without shaking the scale)

What does the scale read? 99kg or 100kg or 99.5kg etc? If it is not 99kg what forces are at play given the mass of the ball and string are now in motion?

It is my notion that the motionless man on the scale reads 100kg because he, the string, and the ball are now one unit. Once the 1kg mass is in motion it becomes external to the unit and the scale reads 99.

What are your thoughts? (this isn't homework, just something that has been bothering me)
Justin

2. Aug 2, 2012

### Drakkith

Staff Emeritus
I believe the scale still reads 100kg. The ball is still being pulled down by gravity. This is why you have to spin something faster to make it rise towards a 90 degree angle. A spinning top doesn't weigh less than one that is stopped and fallen over.

3. Aug 2, 2012

### evowerks

My counter to the comparison of the top is that the top was and remains one unit so to speak. If the scale reads 100 how is that 1kg being transferred to the scale? If the string is horizontal how is the weight on the scale the same?

4. Aug 2, 2012

### Drakkith

Staff Emeritus
The weight is being pulled down by gravity, no matter if it is spinning or not. The string is near horizontal because of centrifugal force, not because the force of gravity has lessened. It is still pulling down on the string just as much as it was when it was stopped. You just have 2 different forces now instead of one.

5. Aug 2, 2012

### evowerks

Who was it that said "Give me a place to stand and I can move the world"? I'm just not as confident as you are on this. Astronauts experience weightlessness in orbit but there is about the same amount of Earth's gravity on them as us on the ground. They don't experience the sensation of weight because they have nothing to "stand on". If you are right than we must conclude the horizontal string still transfers 1kg to the scale as it would vertically. I just can't get past that concept.

6. Aug 2, 2012

### Staff: Mentor

It is still 100 kg. You can convince yourself of this simply by drawing some free body diagrams. You still have to exert a 10 N force up on the string to keep the ball from falling. By Newton's 3rd law that results in a 10 N force down on your hand. The force on the scale is then your weight plus those 10 N.

7. Aug 2, 2012

### cjl

The reason is that the string isn't horizontal. The string is slightly below horizontal, with a 1 kgf vertical component to the tension (plus a much larger horizontal component which will depend on how fast the string is being swung).

8. Aug 3, 2012

### evowerks

So what you are saying is that it doesn't matter how fast the weight is spinning because you are still pushing up the 1kg anyway? Let's change the scene a bit. Let's say the man holds a high speed electrical motor attached to a string and weight, again with the string and weight equaling 1kg for a total of 100kg (man, motor, batteries, string, weight).
He holds the motor overhead and spins the weighted string...Same outcome? 100kg?

9. Aug 3, 2012

### Staff: Mentor

No. You have to include the weight of the motor and batteries.

10. Aug 3, 2012

### evowerks

apology. What I meant to say is that the man got thinner and he now weighs 99kg whilst holding the motor and batteries. :)

11. Aug 3, 2012

### Drakkith

Staff Emeritus
Same outcome. It's still 100 kg.

12. Aug 3, 2012

### Staff: Mentor

Then it would be 100 kg. Whatever the total mass is of all the things on the scale is what the scale will read. Spinning in a horizontal circle does not cause antigravity, otherwise we would have built vehicles on that principle.

13. Aug 3, 2012

### mikeph

It doesn't matter how fast he spins it, the strong cannot be horizontal. The vertical component of the tension in the strong (acting on the ball) must be nonzero to cancel the ball's weight. If the string is horizontal, the ball will accelerate downwards.

14. Aug 3, 2012

### Staff: Mentor

That is true. When books talk about horizontally spinning weights it should be understood that the ball is spinning in a horizontal plane, but the string necessarily rises above this plane for the reason you gave here.

15. Aug 3, 2012

### evowerks

I guess I didn't realize that the string would never become horizontal relative to the hand/motor...
DaleSpam, that's kind of what I was getting at. The mass of the ball is unchanged, but I was debating if the weight perceived at the scale would change given the weight is possibly external to the unit.

16. Aug 3, 2012

### Drakkith

Staff Emeritus
A good question to ask yourself is "What is holding the ball up against gravity?". The answer of course is the string and the person.

17. Aug 3, 2012

### pgardn

The red part is an important addition. As anyone who stands on a scale knows if you crouch down and then stand up quickly, your weight appears to change. Its fairly difficult to stand really still on a digital scale that reads to the 0.1 pounds, and not have it change some...

18. Aug 5, 2012

### evowerks

OK. We seem to have a consensus that the scale would indeed read 100kg. I think the concept I was missing was that the spinning weight is not on the same plane as the center. (i.e. not horizontal) It makes sense that the weight can be transferred down to the scale given the vertical component of the string is still present. Thanks to all for the input.

J

19. Aug 6, 2012

### Grizzled

Krrrhm, a small correction folks. I submit that if the scale in questison is properly constructed, it will register MORE than 100kg. You all forgot horizontal force applied to the scale!

What prevents that ball from flyng away? String tension. Where does THAT come from? Well, via the man and the soles of his feet, ultimately - it's friction with the scale surface. Spin that ball fast enough and it can pull you off the scale...together with your electric contraption :-)

So, if your scale can measure horizontal as well as vertical forces applied to it, the total will be more than 100. How much more - depends on rotation speed. The resulting force vector will be rotating around the vertical and the angle - how far off the vertical it is, also depends on the speed.

Last edited: Aug 6, 2012
20. Aug 6, 2012

### Drakkith

Staff Emeritus
How does a horizontal force make a scale have a higher reading?

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