If a belt drive has a driven pulley with diameter twice the driver, which statement is true about the relation between ω1 and ω2?

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Multiple Choice

If a belt drive has a driven pulley with diameter twice the driver, which statement is true about the relation between ω1 and ω2?

Explanation:
In a belt drive with no slip, the belt’s linear speed is the same at both pulleys: v = ω1 r1 = ω2 r2. If the driven pulley’s diameter is twice the driver’s, its radius is twice as large, so r2 = 2r1. Substituting gives ω1 r1 = ω2 (2r1). Canceling r1 leads to ω1 = 2 ω2. So the driver must rotate twice as fast as the driven pulley.

In a belt drive with no slip, the belt’s linear speed is the same at both pulleys: v = ω1 r1 = ω2 r2. If the driven pulley’s diameter is twice the driver’s, its radius is twice as large, so r2 = 2r1. Substituting gives ω1 r1 = ω2 (2r1). Canceling r1 leads to ω1 = 2 ω2. So the driver must rotate twice as fast as the driven pulley.

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