This code was an answer to a forum question asking for a touch to drag an object but a tap-touch to rotate the object. I kept it simple and without reference to my mathlib.lua for the sake of brevity.

simple drag and rotate demo.lua

local function angleOnTarget( e )
	local a = math.atan2( e.y-e.target.y, e.x-e.target.x ) * 180 / (4*math.atan(1))
	if (a<0) then a=a+360 end
	return a
end

local function tap(e)
	e.target.touchMode = "drag"
	print("drag mode")
	e.target.dragtimer = timer.performWithDelay( 400, function()
		e.target.touchMode = "move"
		print("move mode")
	end )
	return true
end

local function touch(e)
	if (e.phase == "began") then
		e.target.hasFocus = true
		display.currentStage:setFocus( e.target )
		e.target.touchMode = e.target.touchMode or "move"
		e.target.prev = e
		if (e.target.dragtimer) then
			timer.cancel( e.target.dragtimer )
			e.target.dragtimer = nil
		end
		e.target.prevangle = angleOnTarget( e )
		return true
	elseif (e.target.hasFocus) then
		if (e.phase == "moved") then
			if (e.target.touchMode == "move") then
				e.target.x, e.target.y = e.target.x+(e.x-e.target.prev.x), e.target.y+(e.y-e.target.prev.y)
			else
				local angle = angleOnTarget( e )
				e.target.rotation = e.target.rotation + (angle - e.target.prevangle)
				e.target.prevangle = angle
			end
			e.target.prev = e
		else
			e.target.hasFocus = nil
			e.target.prev = nil
			display.currentStage:setFocus( nil )
			e.target.touchMode = "move"
			e.target.prevangle = nil
		end
		return true
	end
	return false
end

local rect = display.newRect( display.contentCenterX, display.contentCenterY, 300, 150 )

rect:addEventListener( "touch", touch )
rect:addEventListener( "tap", tap )