SEARS kENMORE washer Model #110.92279100

This is a symptom of a broken motor coupling. The following link provides you with step-by-step instructions on how to replace one:

http://www.fixya.com/support/r385250-replacing_motor_coupling_kenmore_top

Many of the original motor couplings were all made of plastic. The center hole that mounts on the drive motor shaft would start to form cracks and eventually break. A new modified motor coupling was manufactured with a steel grommet to prevent this from happening. The link has the new part number at the bottom of the page. You can order this part online at searspartsdirect.com by typing in your model number and locating item number 13 under the "Brake/Clutch/Gearcase/Motor and Pump" heading. Or, take the part number provided to your nearest appliance parts retailer. This is a common part they do carry.

I hope you find this information helpful. Let me know if you have questions or require additional assistance.