Turn the shaft by hand. If it rotates freely, then the bearings should be okay. (Remember to turn in the same direction that the motor would naturally turn.)
If the shaft doesn't turn freely, then there are a host of possibilities. This include, but not limited to,:
1. Bearing(s) seizing.
2. The rotor is binding on the stator. (For those less into this: the rotor is the rotating part and the stator is the stationary part.)
3. The brushes may be shot or "missing." ("Missing" referring to the brushes having come out of their holders.)
The burning smell can come a number of sources, including:
1. Bad brushes.
2. Bad commutator (the place where the brushes run against.)
3. Breakdown of the insulation on the wires in the motor.
4. Friction on contaminants between the rotor and the stator.
5. Bad bearings. (I don't believe that bad bearings would be the culprit.)
If one is mechanically inclined with regards to motors, one could remove the rotor and inspect for the above items.
1. If the windings haven't burned, then proceed to below. Otherwise, either have the motor unit rewound or scrap the motor unit.
2. If bad bearings, just buy a new set and do the repair.
3. If bad brushes, just buy a new set and install.
4. If foreign body (e.g. sawdust) is trapped between the rotor and stator, remove the foreign body.
I highly recommend the Bosch 1617EVSPK kit. Mine has given good service.
Hope this helps,