Are there any rules that specify whether or not switching weapons in combat takes up an action?
Yes, there are.
You can also interact with one object or feature of the environment for free, during either your move or your action. For example, you could open a door during your move as you stride toward a foe, or you could draw your weapon as part of the same action you use to attack.
If you want to interact with a second object, you need to use your action. Some magic items and other special objects always require an action to use, as stated in their descriptions.
[PHB, Chapter 9: Combat, The Order of Combat, Your Turn, Other Activity on Your Turn]
A shield takes 1 Action to don and 1 Action to doff. [PHB, Chapter 5: Equipment, Armor and Shields, Getting Into and Out of Armor]
Many GMs allow you to carelessly drop an object at any time (it makes sense not to require any Action to just open your hand and let go).
So, in your question, it would take a round to doff the shield before you could even start to pick up a bow and use it.
You can stow or draw a weapon as a free interaction while moving or making an attack. Dropping a weapon is a valid option. (Had a fun moment in my last session where my barbarian had stowed a handaxe on one turn and dropped the other (mic drop style) before pulling out his greataxe while tilting his head to the side to really let those goblins know that it was on.)
So, in your question, it would take a round to doff the shield before you could even start to pick up a bow and use it.
The other issue here is that there's no sensible way to carry a bow (or most of the weapons with the two-handed property for that matter) on your body - especially if you've already got a backpack full of adventuring gear on your back. If it's not a one-handed weapon you're most likely going to be carrying it by hand (and even then, one-handed pole weapons like spears and quarterstaves had to be carried by hand too.)
are there any ruling about using a throwing weapon with fighter extra attack. the scenario is i am a level 8 fighter. i killed an enemy with the first attack with my great sword and attempted to throw a dagger with my second attack from the same action. i was told this wasn't allowed because i had to use both attacks with the same weapon. in my minds eye i could draw the dagger from holsters strapped to my armor and throw with one hand while keeping one hand on the hilt of my great sword, but its not allowed because i have to use both attacks with the same weapon. is there a specific ruling either way ?
are there any ruling about using a throwing weapon with fighter extra attack. the scenario is i am a level 8 fighter. i killed an enemy with the first attack with my great sword and attempted to throw a dagger with my second attack from the same action. i was told this wasn't allowed because i had to use both attacks with the same weapon. in my minds eye i could draw the dagger from holsters strapped to my armor and throw with one hand while keeping one hand on the hilt of my great sword, but its not allowed because i have to use both attacks with the same weapon. is there a specific ruling either way ?
There is no rule saying that both of your attacks in the same Attack action have to be with the same weapon.
This has been clarified in Sage Advice here, which says:
When you use Extra Attack, do you have to use the same weapon for all the attacks?
Extra Attack imposes no limitation on what you use for the attacks. You can use regular weapons, improvised weapons, Unarmed Strike, or a combination of these options for the attacks. However, you must still follow the rules for equipping and unequipping weapons as part of the Attack action.
It's also worth noting that two-handed weapons only need you to have two hands on them while you're actually making an attack with them; you can hold a greatsword in one hand while doing something else with the other hand just fine.
Are there any rules that specify whether or not switching weapons in combat takes up an action? For example:
If I'm wielding a shortsword and shield one turn, can I make a bow attack next turn without using an action to change equipment?
Could I switch the shield with another shortsword and still make two attacks with the shortswords?
Yes, there are.
[PHB, Chapter 9: Combat, The Order of Combat, Your Turn, Other Activity on Your Turn]
A shield takes 1 Action to don and 1 Action to doff. [PHB, Chapter 5: Equipment, Armor and Shields, Getting Into and Out of Armor]
Many GMs allow you to carelessly drop an object at any time (it makes sense not to require any Action to just open your hand and let go).
So, in your question, it would take a round to doff the shield before you could even start to pick up a bow and use it.
You can stow or draw a weapon as a free interaction while moving or making an attack. Dropping a weapon is a valid option. (Had a fun moment in my last session where my barbarian had stowed a handaxe on one turn and dropped the other (mic drop style) before pulling out his greataxe while tilting his head to the side to really let those goblins know that it was on.)
The other issue here is that there's no sensible way to carry a bow (or most of the weapons with the two-handed property for that matter) on your body - especially if you've already got a backpack full of adventuring gear on your back. If it's not a one-handed weapon you're most likely going to be carrying it by hand (and even then, one-handed pole weapons like spears and quarterstaves had to be carried by hand too.)
The Forum Infestation (TM)
are there any ruling about using a throwing weapon with fighter extra attack. the scenario is i am a level 8 fighter. i killed an enemy with the first attack with my great sword and attempted to throw a dagger with my second attack from the same action. i was told this wasn't allowed because i had to use both attacks with the same weapon. in my minds eye i could draw the dagger from holsters strapped to my armor and throw with one hand while keeping one hand on the hilt of my great sword, but its not allowed because i have to use both attacks with the same weapon. is there a specific ruling either way ?
There is no rule saying that both of your attacks in the same Attack action have to be with the same weapon.
This has been clarified in Sage Advice here, which says:
It's also worth noting that two-handed weapons only need you to have two hands on them while you're actually making an attack with them; you can hold a greatsword in one hand while doing something else with the other hand just fine.
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