Like the title. Say I was weightless and motionless in a sealed vacuum. I’m wearing a spacesuit and holding a DustBuster tm.
I switch the handy household gadget on.
Do I move?
What is it sucking?
If there is a bag on the exhaust, does it inflate?
Thanks
You don’t move, it’s not sucking anything, and the bag doesn’t inflate. Next question?
You might move the tiniest bit from the torque of the fan spinning. But it sucks nothing because there is nothing to suck.
Yep, you’d start to rotate around the axis that the motor/fan are spinning on.
Until you turn it off. Then you’d stop rotating. You just invented a reaction wheel!
Is that how they navigate in space suits? By carrying dustbusters to outer space?
Are you sure?
Yes. You only spin left as long as the motor in the dustbuster is spinning right. If you kept spinning left when the motor stopped spinning right, you’d have a perpetual motion machine. If instead you threw pebbles into space to start yourself spinning you’d never stop because the pebbles don’t stop.
And a dustbuster works by moving air with a fan. If there’s no air or fluid, the dustbuster doesn’t suck up anything.
um… what force would be acting on your rotation to stop it, once you turned the fan off?
The motion of the rotor in the motor.
Think about it. The motor/fan starts to slow down. Why does it slow down? Because of friction on the parts, sure. And so the motor’s spin is transferred to the body of the dustbuster and the motion of the dustbuster is transfered to your arm.
The motor spinning up clockwise sends you spinning counterclockwise (just a lot more slowly). For the motor to stop spinning clockwise there has to be some counterclockwise force acting on it to stop it, in this case friction. That counterclockwise force slowing down the motor puts a clockwise force on your body, which stops you from spinning counterclockwise.
If there’s little or no friction to slow it down, then the motor keeps spinning clockwise even though the power is off, and you keep spinning counterclockwise. However, since the fan/motor is physically connected to the rest of the dustbuster by bearings or whatever, eventually the spin is going to slow and your spin will slow in the exact same proportion.
The basic principle at work here is conservation of angular momentum. You, plus the dustbuster housing, plus the dustbuster impeller/rotor, have a grand total angular momentum of X. If nothing is rotating at the start of this scenario, then we’ll say X = 0.
Now you push the “on” button. The dustbuster housing applies torque to the impeller/rotor, causing it to begin rotating one way. Newton’s third law says that when the housing applies a torque to the rotor, the rotor applies an opposite torque to the housing. So now the housing - along with you, since you’re gripping it firmly - begin rotating in the opposite direction, but very slowly since you’re much more massive than the impeller/rotor. Because angular momentum of the whole system is conserved, X is still zero: if you add up the angular momentum of the impeller/rotor spinning one way, and the housing + you spinning the other way, they’ll sum to zero.
Now you release the “on” button. Friction in the motor bearings and commutator brushes applies a torque to the impeller/rotor, decelerating it. Newton’s third law again means that the impeller/rotor applies an equal and opposite torque to the housing+you. When the impeller/rotor comes to a stop, so do you. Conservation of angular momentum says this must be so: X was zero when we started, it was zero when the impeller/rotor was spinning, and now it’s still zero. You may have rotated to a new orientation (and so has the rotor), but when everything’s done, you are no longer rotating (again assuming you weren’t rotating when this all started).
Also, the motor would overheat pretty quick.
So, because the hoover hits it’s top speed in say, less than 1 second, I’d also hit my top speed at the same time and stop at the same time it stops?
Exactly correct.
Is the top speed governed electronically, or by air resistance? If the latter, then it’ll just keep accelerating in a vacuum…
Maybe not adding much to the discussion, but I’ll note that if you turn on a DustBuster here on Earth, you can feel it twist slightly in your hand when it starts. The only reason you don’t start rotating is because of friction of your feet against the ground. (In fact, your feet impart a torque to the Earth and the whole Earth starts rotating a little in the direction opposite the DustBuster rotor, but of course it’s so minuscule as to be unmeasurable.) When you turn it off you can feel it twist slightly in the opposite direction.
It shows that this discussion is not just torque.
To be clear, when I said that you wouldn’t move, I meant you would have no linear motion. Others are correct to say that you would spin.
Actually it depends on the design of the device. If it had two motors rotating in opposite directions, you wouldn’t spin. But I doubt there are any actual DustBusters or similar devices that operate that way.
As the physics questions have been answered, let’s look at some of the engineering aspects :