B The Effect of Linear and Rotational Motion on Measured Weight

[Pleiades7]

Consider an extremely long and perfectly calibrated scale. A car with a mass of 1000 kg is placed on it, and the scale registers this weight accurately. Now, suppose the car begins to move, reaching very high speeds. Neglecting air resistance and rolling friction, if the car attains, for example, a velocity of 500 km/h, will the scale still indicate a weight corresponding to 1000 kg, or will the measured value decrease as a result of the motion?

In a second scenario, imagine a person with a body mass of 70 kg standing on a scale while holding two 5 kg weights, one in each hand. The total reading on the scale is therefore 80 kg. If the person then begins to rotate rapidly around their own vertical axis, the arms will extend outward as the weights experience an increasing centrifugal effect. In this state, the acceleration of the weights becomes largely horizontal rather than vertical. Would this redistribution of forces alter the total normal force on the scale, and consequently, the measured weight?

This setup can also be modeled mechanically: two equal masses are attached to opposite ends of a rotating rotor, which is placed on a scale and spun at high angular velocity.

The central question, therefore, is whether any object rotating rapidly about its own axis in a plane parallel to the ground exhibits a measurable reduction in its apparent weight due to the redistribution of centripetal and normal forces.

 

[russ_watters]

Motion has no impact on weight, classically.

The only sorta exception is a vertical oscillation/unbalanced rotation would cause the reading to oscillate.

 

[PeterDonis]

will the measured value decrease as a result of the motion?

Why would it? Tangential motion doesn't affect the normal force.

In this state, the acceleration of the weights becomes largely horizontal rather than vertical.

The direction of the acceleration vector does, yes. But the magnitude of that vector also increases, in such a way that the vertical component, which is what affects the reading on the scale, remains the same.

Would this redistribution of forces alter the total normal force on the scale, and consequently, the measured weight?

No. Again, why would it? That would amount to the person being able to lift themselves by spinning around with weights.

 

[Ibix]

Actually, if the car is moving in a straight line (or, to be precise, has its steering straight at all times) on Earth I think its measured weight will decrease slightly - in fact, it will reduce to zero when the car's velocity is equal to orbital velocity at ground level (which I make to be about 60 times the suggested 500km/h, so this is very much a negligible effect for highway speeds). This isn't anything to do with rotational motion, and in fact I would not expect the effect if the car were driving in a circle (any circle smaller than a great circle anyway).

The spinning weights one likewise has no effect.

 

[wrobel]

It seems I know the origin of the question:

 

[PeroK]

Consider an extremely long and perfectly calibrated scale. A car with a mass of 1000 kg is placed on it, and the scale registers this weight accurately. Now, suppose the car begins to move, reaching very high speeds. Neglecting air resistance and rolling friction, if the car attains, for example, a velocity of 500 km/h, will the scale still indicate a weight corresponding to 1000 kg, or will the measured value decrease as a result of the motion?

Newton's laws of motion involve force, mass and acceleration. They do not involve the velocity of an object. Note that velocity is relative (to a frame of reference). The force on a car is the same whether you consider the car to be at rest or moving. The force depends on the acceleration of the car and not its velocity.

 

[Lnewqban]

If the person then begins to rotate rapidly around their own vertical axis, the arms will extend outward as the weights experience an increasing centrifugal effect. In this state, the acceleration of the weights becomes largely horizontal rather than vertical.

Because there is the vertical constant acceleration of gravity, the direction of the total acceleration of the weights, regardless its magnitude, can never reach a horizontal direction.

 

[A.T.]

Would this redistribution of forces ...

You are confusing relative comparisons and absolute force values. Just because the relative comparison of vertical and horizontal the forces changes, doesn't mean that the absolute value of the weight force changes.

 

[Dale]

it will reduce to zero when the car's velocity is equal to orbital velocity at ground level

That was my thought too.

In this state, the acceleration of the weights becomes largely horizontal rather than vertical. Would this redistribution of forces alter the total normal force on the scale, and consequently, the measured weight?

Classically, no. The total mass is unchanged, as is the acceleration of the center of mass. So the net force is also unchanged.