I have a Kenmore Washing machin 80 series and it won't spin. When I put it on spin it just makes a humming sound. Does this machine have a belt or could it be my transmission

For rotating and spinning the same motor is used, though with different windings.
Both sections have their own start capacitor.
Most probably the start capacitor has to be replaced. Not too expensive, and available from every same-brand supplier.
Sears also can provide maintenance and repair manuals, and spareparts.
The Sears Service website

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