Mechanics Gear A drives Gear B. Gear A has a teeth and speed...

Mechanics Gear A drives Gear B. Gear A has $a$ teeth and speed $r_{A}$ in revolutions per minute $(r p m) .$ Gear $B$ has $b$ teeth and speed $r_{B} .$ The quantities are related by the formula $a r_{\mathrm{A}}=b r_{\mathrm{B}}$ Gear $\mathrm{A}$ has 60 teeth and speed 540 $\mathrm{rpm} .$ Gear $\mathrm{B}$ has 45 teeth. Find the speed of Gear $\mathrm{B}$ .

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Key Concepts

Gear Ratio

The gear ratio is a relation that compares the number of teeth on two gears. It determines how the rotational speed of one gear is modified when transmitted to another. Specifically, the ratio of the teeth numbers between two interlocking gears governs the multiplication or reduction of angular speed in a system.

Inverse Relationship between Teeth Count and Rotational Speed

In a gear system, there exists an inverse relationship between the number of teeth on a gear and its rotational speed. A gear with more teeth will rotate slower than one with fewer teeth if they are meshed together and driven by the same force, preserving the product of the number of teeth and the gear's rotational speed.

Rotational Speed (RPM)

Rotational speed, measured in revolutions per minute (RPM), quantifies how many full turns a gear makes in one minute. It is a key parameter in analyzing mechanical systems and is directly influenced by the gear ratio and the corresponding number of teeth on the gears.

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