Is a torn power cable something that I need to address?
The rubber cable casing has broken/torn. Is this something that needs to be replaced? Can it lead to further problems?
A torn cable can impede the electrical connection to the power source, and it could also be very dangerous. The tear will affect the power flow through the cord, and it could cause extensive heat damage. You should replace the cable.
Also take a look here for troubleshooting the angle grinder.
Torn or cut power cables pose a shock hazard. They are really inexpensive to replace and easy if you have a screwdriver. This is a no-brainer.