How can I "yank" a part down?

How can I “yank” a part down using scripts (preferably not physics) like this? (not as hard though, and with it smoothly rotating back normal)

You could use tweening for the rotation.

Well I guess I could, but I have no idea what easing style, direction, and time to use.

If you want to create a yanking effect, you can create a linear velocity instance on the part and then remove it quickly after, but that’s technically physics. Another way is to tween with a easing style of “Exponential” and a direction of “Out”. One last way I can think of is to use a lerp in an a while true loop inside of a function, ill give an example below.

-- I did this in like 4 seconds sorry if its bad but this is basically what you would do for lerping, tweening would be best option though.
local function yank(object)
	local LerpProgress = 0
	while true do
		if LerpProgress <= 25  then
			LerpProgress = LerpProgress + .1
			wait(.01)
		else
			LerpProgress = LerpProgress + .1
			wait(.05)
		end
		if LerpProgress >= 100 then
			break
		end
	end
end
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TweenService would be the simplest approach to this.

Here is a graph of different easing styles, with direction shown at the bottom.

You will figure out what time to use just by tweaking it, but from the video shown I can probably predict it would be less than or equal to one.

I suggest reading this, however if you need more help I can assist you with the actual scripting

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I really like the People Playground Video

Do a motor would be easy and easy to configure