# Pure Rotation

### Gears and belts

**Belts:**The velocity (v) and tangential acceleration (a_{t}) of the belt must be the same at any point along the belt. The normal acceleration will change depending on the pulley radius.**Gear:**The velocity (v) and tangential acceleration (a_{t}) of the contacting point on both gears are equal. The normal acceleration will change depending on the gear radii. The gear radii ratio of two meshing gears is dependent on the ratio of the number of gear teeth (N).

### Gear and belt equations

Based on the gear and belt properties listed above, we can derive the following equations.

**Angular velocity:**v = r_{1}ω_{1}= r_{2}ω_{2}**Gear teeth relationship:**N_{1}ω_{1}= N_{2}ω_{2}**Angular acceleration:**a_{t}= r_{1}α_{1}= r_{2}α_{2}