Motor runs but rear wiper doesn't move

During recent cold/ice spell, went to use my rear wiper and heard a pop (there was ice around the wiper base), then the wiper was flipping all over the place. Now I can hear the motor running but the wiper doesn’t move. Plus, I can easily move it around by hand - no resistance. Do I have to replace the whole motor or is there possibly a gear or linkage between the motor and arm that stripped or popped away, so that can be fixed? 2002 Hyun Accent.

If your lucky, the splines on the wiper arm are stripped, and the splines on the wiper motor are OK. This means just replacing the wiper arm will fix this. Otherwise, you may need to replace the motor as well. The motor assembly is a sealed unit, and simply cheaper and easier to replace the motor unit than to try and rebuild it yourself.

Thank you for your speedy response. Is there an easy way of checking this, I have only basic tools but have an honest mechanic. Weather calls for quick fixing, but if I take it in and find out it’s the motor, then have to wait or pay the mechanic’s price for the motor. My thought was to buy the motor online and take it to the mechanic (or isn’t that done)?

You can try to replace the wiper arm yourself, but if you have not worked on cars before you may want your mechanic to handle it. Taking the parts to a mechanic is like taking eggs and bread to the diner and asking them to make breakfast for you. The mechanic can usually get the part cheaper than you can, and does mark it up, but he needs to make a living and stay in business. The next time you have snow and ice built up around the wipers, gently break them free from the windshield to prevent breaking the motor or spline

The main lesson from this entire story is to NEVER hit the switch for the rear/front wipers, untill they have been thoroughly dislodged and cleaned from the ice/snow they get encased in, during such winter weather.
Yes, this will involve several uncomfortable minutes in the freezing cold weather, but it is a lot cheaper than dealing with wiper assembly issues.

If there is plastic cover at the end of the wiper arm pop it up and turn on the motor. if the shaft/mounting nut turns it is most likely the wiper arm splines that are stripped.