To maintain equal linear velocity among gears, the smaller gear must rotate faster.

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Multiple Choice

To maintain equal linear velocity among gears, the smaller gear must rotate faster.

Explanation:
When two gears mesh, the tangential (linear) speed at the point where they touch must be the same for both gears. That speed is v = ω r for each gear. Since the smaller gear has a smaller radius, it must spin faster (have a larger angular velocity) to achieve the same tangential speed as the larger gear. Put simply, ω_small × r_small = ω_large × r_large. Because r_small < r_large, it follows that ω_small > ω_large. So the smaller gear must rotate faster to maintain equal linear velocity at the contact.

When two gears mesh, the tangential (linear) speed at the point where they touch must be the same for both gears. That speed is v = ω r for each gear.

Since the smaller gear has a smaller radius, it must spin faster (have a larger angular velocity) to achieve the same tangential speed as the larger gear. Put simply, ω_small × r_small = ω_large × r_large. Because r_small < r_large, it follows that ω_small > ω_large.

So the smaller gear must rotate faster to maintain equal linear velocity at the contact.

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