Will all the dominoes fall? The purpose of this challenge is to figure out whether all the dominoes will fall, given an input string representing a top view of the table.
Input format
The program can take the input as a single string with newlines or a list of strings. Spaces denote, well, empty spaces, and the rest represent dominoes.
The start domino and the direction the dominoes start to fall will be denoted by one of &lt;(left),&gt; (right), ^ (up), v(down). There will be exactly one start domino in the input.
The other dominoes will be represented by one of the following four characters:

| - falls right when pushed from the left, falls left when pushed from the right
- - falls up when pushed from the bottom, falls down when pushed from above
/ - falls right when pushed from the top and vice versa, falls left when pushed from the bottom and vice versa
\ - falls left when pushed from the top and vice versa, falls right when pushed from the bottom and vice versa.

Basically, | and - keep the momentum going in the same direction, and the slashes (/ and \) cause quarter-turns.
Dominoes may not fall twice. If a domino falls, you may consider that an empty space in the next iteration.
Pushing - from the left or right and pushing | from the top or bottom are undefined behavior.
Output
A truthy/consistent value if all the dominoes will fall, and a consistent falsy value otherwise
Here's an example to make it a bit more clear (o represents a fallen domino for the sake of this example):
Step 1 - Starts at the 4th domino in the first row
\||&lt;
-
-  -
\||\

Step 2 - start domino has fallen
\||o
-
-  -
\||\

Step 3 - Go left because start was '&lt;'
\|oo
-
-  -
\||\

Step 4 - keep going left
\ooo
-
-  -
\||\

Step 5 - keep going left
\ooo
-
-  -
\||\

Step 6 - keep going to left, will go down next
oooo
-
-  -
\||\

Step 7 - change direction, go down because of '\'
oooo
o
-  -
\||\

Step 8 - keep going down
oooo
o
o  -
\||\

Step 9 - go down, will go left next because of '\'
oooo
o
o  -
o||\

Oops! Can't go any further, so output should be a falsy value

Rules
Just to clarify, there's no gravity or anything. The direction depends on the position of the domino (/, \, |, or -)
This is code-golf, so shortest code in bytes wins.
More test cases:
Truthy
&gt;
_________________________________________________________

\|||&lt;
-
-
/|||
__________________________________________________________

     \|/
     /|/
       -
       -
    \||\
    ^

Falsy
\|/
- -
/|/|  &lt;-This last '|' doesn't fall, because the '/' before it has already fallen once
  ^
__________________________________________________________

|&lt; |  &lt;- This last '|' doesn't fall, because the dominoes don't wrap around.
__________________________________________________________

&gt;||\||   Because after the '\', it tries to go up

Undefined behavior:
&gt;-       Can't push '-' from the left
```
Charcoal, 86 69 bytes
ＷＳ⊞υι≔⪫υ¶θ≔v&gt;^&lt;ηＰθ…θ⌈Ｅη⌕θιＷ№ηＫＫ«↶⊗⁺³⌕ηＫＫ≔ⅈι ≔§⪪\-//|\³⁻ⅈιη»≔⌈ＫＡθ⎚→‹θ!

Try it online! Link is to verbose version of code. Outputs a Charcoal boolean, i.e. - if all the dominoes fall, nothing if some remain. Explanation:
ＷＳ⊞υι≔⪫υ¶θ

Input the table as an array of strings and join them together.
≔v&gt;^&lt;η

Make a string of rotations for the starting domino characters. The string starts with the character for a clockwise rotation, then the one for no rotation, then an anticlockwise rotation, then a u-turn.
Ｐθ…θ⌈Ｅη⌕θι

Print the table and then up until the (last) occurrence of one the starting domino characters.
Ｗ№ηＫＫ«

While the current character is present in the table of rotations...
↶⊗⁺³⌕ηＫＫ

... pivot according to the position of the character in the table of rotations (annoyingly I have to spend an extra byte adding 3 instead of subtracting 1 because Charcoal can't pivot by negative amounts)...
≔ⅈι ≔§⪪\-//|\³⁻ⅈιη

... and, temporarily saving the current X-coordinate, erase the current character, moving in the current direction, then choose the list of valid characters (again listed in the order rotate clockwise, don't rotate, rotate anticlockwise) depending on whether the current direction is vertical or horizontal (detected via the change in X-coordinate, since Charcoal has no builtin to read the current direction).
»≔⌈ＫＡθ⎚→‹θ!

Check that only spaces are left.