rear sprocket

take off the left wheel and hub and pull off the whole spindle that the sprocket mounts too, then unbolt the sprocket. you may be able to get the sprocket off by just removing the wheel and unbolting it.

I cant exactly remember.
 
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. The carrier that actually holds the rear sprocket is a lil loose
 
If your refering to the sprocket hub (the part that the sprocket bolts to) being loose, You may need to tighten the 2 big locknuts. If its all tight and its still sloppy, your splings may be worn.
 
Is it loose in the direction of rotation? Or side to side? If side to side you might correct by retightening axle, unless brgs are worn. Have to follow directions else you'll overtighten and blow the brgs
 
Apply Loctite to rear axle threads.

Tighten inner nut to 40 ft lbs to preload the bearings.

Tighten the outer nut whilst holding the inner nut to 140 ft lbs.

Loosen the inner nut whilst holding the outer nut to 170 ft lbs.

If this way is not done there is a possibility of the nuts becoming loose when riding.
 
If you add grease under pressure to the carrier, you must remove the inner factory fitted seal from the bearings.

Leaving the seal in place and adding a zerk is a pointless exrecise as no grease will get to the bearings, and could force the seal against the ballrace and cause bearing failure.

Unless you do water, there is no need to fit a zerk add any extra grease to the carrier bearings.

My take on extra grease, which I believe is not required.
The bearing, itself, consists of an inner race, an outer race, balls and a cage which evenly distributes the balls. Common bearings are designed to allow for a radial load with some limited axial loading. ALL BEARINGS ARE LUBRICATED WITH OIL.
Grease, itself, is an oil sponge. The base (spongy) part of the grease varies depending on the manufacturer, temperature, environment and user preference. The grease holds the oil in suspension and allows the oil to flow during operation. The oil compresses between the bearing balls, inner and outer races and the cage, reducing friction. Ball bearings have small, microscopically rough surfaces on the balls, these surfaces move the oil, holding it to the ball during operation.
When too much grease is added, the grease is compressed between the bearing surfaces, increasing pressure and resulting with heat. Too little grease causes the surface friction to increase, resulting with heat.

If a bearing heats up any extra grease that cannot be contained within the seal will be expelled.
When the bearing cools the grease will be drawn back into the bearing, if there is any contamination of the expelled grease by water or dirt, this will be drawn back into the bearing, eventually causing its destruction.

The manufacturer puts adequate grease in their bearings. Just enough to allow expansion without expulsion, and enough for lubrication.