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Does spinning an object make it heavier?

A real-world example:

I was mowing the lawn in front of my house, a lawn that tends to have some steep inclines. I realized that the lawn-mower was easier to move, and much easier to pull up inclines when it was off than when it was running. The only difference between a lawn-mower that's running and one that is isn't is that the blade is rotating and there's some electricity running through it as it uses up gas. I guess the most significant of those would be the spinning blade.

Does the spinning blade make the lawn-mower heavier as a whole object, and would that mean that spinning objects are heavier than non-spinning objects?

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3 Answers 3

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As in the answer of @Mark Eichenlaub the mass of the lawnmower won't increase! Of course the blades of the lawnmower can have a pull-effect in which they might aid your foreward-movement (in which degree this might help, I'm not sure ...).

Of course a rotating blade creates an angular momentum, so if you were to make a turn with your lawnmower you'll need some extra force to change this momentum. So I'd say that turning would be harder! Also if your lawn is uneven, your lawnmower might tilt which will of course also change your angular momentum, this might make it harder to go in a foreward direction!

So yes spinning can make an object heavier (in the sense that you'll need to apply a bigger force), but only if you'll work against it's angular momentum or try to change the direction of rotation! This is actually the working principle of a gyroscope. A nice youtube-film about another real-life application (aircraft) is found here. A third real-life example is riding a bike ! Due to the spinning of the weels it's easy to stay in an upright position (or hard to fall), once you stop this is no longer the case!

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    $\begingroup$ On uneven ground more often than not "you'll work against its angular momentum or try to change the direction of rotation" That is what creates the illusion of heavier for a spinning object.(relativistic changes are minuscule and cannot be felt) $\endgroup$
    – anna v
    Commented Sep 10, 2013 at 13:18
  • $\begingroup$ @annav relativistic effects are indeed miniscule (unless Zolani13 mows his lawn at almost lightspeed of does the mowing with a rotating black-hole which would be bad news for all of us). But indeed an uneven ground might make it heavier because of the change in angular momentum. I'll edit it immediately ! $\endgroup$
    – Nick
    Commented Sep 10, 2013 at 15:17
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No, a lawn mower is not heavier when spinning in any significant way. If it is harder to push, this is probably because of friction working against rotation of the wheels.

In theory, the lawn mower has slightly-higher mass when spinning according to $E = mc^2$. For a spinning lawn mower this is on the order of $10^{-16}$ the mower's weight, or $10^{-12}$ grams. The number comes out small because the blades are moving slowly compared to the speed of light. Additionally, the lawn mower in practice loses much more mass than this when the blades start spinning due to exhaust from the gas.

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  • $\begingroup$ +1: Of course it is. IIRC, this was addressed by Feynman in one of his lectures. It becomes clear if people stick to the fact that mass is invariant. Though it's universally true, amateurs can at least digest that *mass doesn't change at normal velocities, very much less than $c$ ;-) $\endgroup$
    – Waffle's Crazy Peanut
    Commented Sep 10, 2013 at 2:43
  • $\begingroup$ @CrazyBuddy: The mass of a particle is invariant, but the wheel isn't a particle, and mass isn't additive. The mass of a spinning wheel is higher relativistically. $\endgroup$
    – user4552
    Commented Sep 10, 2013 at 4:43
  • $\begingroup$ It's theoretically possible that the blades of the mower are acting like helicopter blades sucking the mower to the ground, but it still wouldn't be very much. $\endgroup$
    – Chachmu
    Commented Sep 10, 2013 at 14:34
  • $\begingroup$ @BenCrowell Really? Do we not define the mass of a system of particles as the sum of the masses of all particles in the system? When you make the claim about non-additivity of mass, do you have in mind squaring the total four-momentum and calling the result the mass of the system? I'm admittedly quite confused. $\endgroup$
    – joshphysics
    Commented Sep 13, 2013 at 1:17
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    $\begingroup$ @joshphysics: When you make the claim about non-additivity of mass, do you have in mind squaring the total four-momentum and calling the result the mass of the system? Yes, exactly. So, e.g., two EM wave packets with energy-momentum vectors $(p_t,p_x)=(E,E)$ and $(E,-E)$ have a total energy-momentum of $(2E,0)$, corresponding to a mass of $2E$. $\endgroup$
    – user4552
    Commented Sep 13, 2013 at 3:14
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during operation the blade in the mower has very high angular momentum. the blade actually spins on a plane parallel to the ground, so depending on cw or ccw spin, the angular momentum points downwards or upwards respectively. this makes the mower detectibly more resistant to changes in pitch(going up or down a hill) or roll (sideways tilt).

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