Because it’s a game, meaning it has rules. Simply homebrew/house rule your idea. You don’t have to follow the books to the letter

The first case assumes that the hand can accelerate continuously. If the max distance it can travel over a period of ~6 seconds is 30 feet, then it can only travel at a maximum speed of about 3.5 MPH. As for the second case, spinning the object, similar logic would apply and the hand would most likely not be able to physically spin fast enough to generate 9 lbs of centripetal force

Can you shove with mage hand?

Quote from Alethalion >>

Can you shove with mage hand?

 Not RAW or RAI, though for that telekinetic shove flavor that you might be looking for, take a look at the Telekinetic feat from Tasha's Cauldron of Everything.

really great but it would be funny if it could pick up weapons and do a melee attack lol

Best use: Flicking off people from 30 feet away.

As an Arcane Trickster Rogue, I was wondering if I could use Mage Hand to handle the ammunition aspect if I was using a Hand Crossbow in one hand, and a Rapier in the other. With the Crossbow Expert feat, the loading is ignored:

• You ignore the loading property of crossbows with which you are proficient.
• Being within 5 feet of a hostile creature doesn’t impose disadvantage on your ranged attack rolls.
• When you use the Attack action and attack with a one-handed weapon, you can use a bonus action to attack with a hand crossbow you are holding.

So can the Mage Hand act as the ammunition support so I can use a Rapier in my other hand for the Defensive Dueling feat?

• When you are wielding a finesse weapon with which you are proficient and another creature hits you with a melee attack, you can use your reaction to add your proficiency bonus to your AC for that attack, potentially causing the attack to miss you.

Quote from FreddyVoorhees >>

As an Arcane Trickster Rogue, I was wondering if I could use Mage Hand to handle the ammunition aspect if I was using a Hand Crossbow in one hand, and a Rapier in the other. With the Crossbow Expert feat, the loading is ignored:

• You ignore the loading property of crossbows with which you are proficient.
• Being within 5 feet of a hostile creature doesn’t impose disadvantage on your ranged attack rolls.
• When you use the Attack action and attack with a one-handed weapon, you can use a bonus action to attack with a hand crossbow you are holding.

So can the Mage Hand act as the ammunition support so I can use a Rapier in my other hand for the Defensive Dueling feat?

• When you are wielding a finesse weapon with which you are proficient and another creature hits you with a melee attack, you can use your reaction to add your proficiency bonus to your AC for that attack, potentially causing the attack to miss you.

That's an interesting question.  First off, I think this is firmly in the "DM's Call" domain.  But if I were your DM, thinking mechanically, I think you could conceivably do that with Mage Hand Legerdemain, though remember that it's a bonus action or an action to control a Mage Hand as an Arcane Trickster Rogue.  So I don't think you could justify doing that and then also taking advantage of the third bullet point from the feat, which is the bonus action attack.  You'd either have to load it with your mage hand as a bonus action or shoot with your bonus action, but not both.  I would be tempted to allow it from a coolness standpoint, but the fact that you're able to wield both a rapier and a hand crossbow and still make an off-hand attack with the crossbow does kind of break the game down mechanically, if you do this precisely how you're suggesting.

Buuuuuuutttt...  

Dropping an item (including a weapon) is a free action, and picking up an item (including a weapon) is considered "Interacting with objects around you" and may be done in tandem with either a move or an action, so you could conceivably drop the rapier, shoot, reload with your now-free hand, and shoot again as a bonus action (because the crossbow no longer has the Loading property) and, whether you actually take any steps or not, to pick up your rapier again as part of your move.

So based on that, I'd probably rule that you could do it, but it would take your one free object interaction on the turn, the same as if you did it with the rapier juggling method described above.  The way I run my table is that you can flavor anything in any way you choose, so long as it does not give you an actual mechanical advantage.

But it's not my call.  It's your DM's.  If you want to provide this as an argument in your favor you can, but keep in mind that your DM has final say on the matter for whatever happens at their table.

That's an illogical reason to prove why RAW says it can't punch. Most PCs races can only move 30ft/6s, some of them even only 25ft/6s, and yet they can all unarmed strike. PCs can also use weapons, which it is assumed you're putting a lot more force into. Yet, the character still has 30ft of "movement speed". Also, all weapons in the PHB, except for the Pike and the Heavy Crossbow are equal to or less than 10 pounds. By all means, a Mage Hand should be able to pick up nearly any weapon (of course, a single mage hand can't use two-handed weapons, but can at least hold them). I don't expect a Mage Hand to use weapons necessarily, but it should at least be able to unarmed strike or shove. The only way I see why it couldn't, is to say that the Mage Hand does not have access to "Actions" only "Free Actions"/Interactables.

TL;DR, Movement speed does not equate to the amount of power a thing can use in a punch or strike.

If you think about it if it was used to pull instead of push it'd be more interesting like useing a save to see if the creature is pulled could lead to a fun moment of someone useing the mage hand to pull someone to an edge

 Tho this is only if mage hand is able to pull something like a weapon out someones hand

Quote from Dungeon101Master >>

If you think about it if it was used to pull instead of push it'd be more interesting like useing a save to see if the creature is pulled could lead to a fun moment of someone useing the mage hand to pull someone to an edge

 Tho this is only if mage hand is able to pull something like a weapon out someones hand

 There's actually a feat in Tasha's Cauldron of Everything called Telekinetic that gives you a half-ASI (mental stats, your choice), mage hand, and the ability to shove telekinetically 5ft directly toward or directly away from you as a bonus action.  Mechanically, it's a separate ability, but I like to imagine it's your mage hand that does the pushing.

Edit: Apparently feats aren't tooltip-able 😅

What if you dropped a 10lb rock from 30ft and it just so happened that an enemy was standing under it? 

Quote from Aelon_Xarr >>

What if you dropped a 10lb rock from 30ft and it just so happened that an enemy was standing under it? 

 This is probably the only way you could conceivably deal damage with this, and I'd probably just award half falling damage for it (10 lbs from 30 feet will have no where near the energy (and hence impart no where near the force) of a 150-300lb humanoid falling the same distance).  Since you can't attack (which represents fine aiming), you're just dropping it and hoping.  The enemy would have to get a dex save to get out of the way (same as I'd rule any free-falling object), and since it's one object and not a spray, it'd be save or suck. 

Still an off-brand use of the spell, but doesn't actually violate any of the rules, so I'd allow it.  But there are far better ways to use an action on your turn.  

I would say it would just be a 1d4 improved thrown weapon attack. Speed doesn't equate to power, and even then a short bow can fire an arrow at at around 150mph and does 1d6. Maybe add spell attack as a bonus damage but still would be pretty ineffective as an attack. Something like magic stones perhaps

it says you can open an unlocked door or container does that mean you  can't unlock a door from behind ?

Would it be reasonable to use mage hand and, if we assume a gray ooze weighs 10 pounds or less, to simply… pick it up and drop it on a hobgoblin’s head? The GM allowed it, and the ooze was making the attack roll, not me

Quote from SplotchTheCat >>

Would it be reasonable to use mage hand and, if we assume a gray ooze weighs 10 pounds or less, to simply… pick it up and drop it on a hobgoblin’s head? The GM allowed it, and the ooze was making the attack roll, not me

 The mage hand specifically discusses picking up objects and nowhere discusses picking up creatures.  If the DM rules that it can, then sure.  But RAW I wouldn't expect this to work.

Quote from VectorVinewhip >>

I would say it would just be a 1d4 improved thrown weapon attack. Speed doesn't equate to power, and even then a short bow can fire an arrow at at around 150mph and does 1d6. Maybe add spell attack as a bonus damage but still would be pretty ineffective as an attack. Something like magic stones perhaps

 The spell specifically states it can't make attacks, which is why I said DEX save to avoid instead of attack roll, but I agree this is semantic. 

Quote from glaedr1 >>

it says you can open an unlocked door or container does that mean you  can't unlock a door from behind ?

 I would generally rule that it's still you manipulating the tools, so you'd have to see it.  And even so, this is a feature given by the Rogue's Arcane Trickster subclass (Mage Hand Legerdemain) so I would rule that you probably wouldn't be able to do that otherwise.

so any point within range? inside someones chest give them a heart massage squeeze the lungs shift around internal organs? yea if allowed this is THE assassins spell

Im just gonna have mage hand drop bricks on people 😊

Can't I just cast it inside of some creature and just "move it around" and do massive damage?