A student set up an experiment to investigate the mechanical properties of a simple two-ge… — ACT

A student set up an experiment to investigate the mechanical properties of a simple two-gear system consisting of a driver gear and a driven gear. The driver gear rotates at a constant speed, while various driven gears with different numbers of teeth, $N$ , are swapped into the system. The student measured the rotational speed, $S$ (in revolutions per minute, rpm), of each driven gear. The table below shows the results of the experiment:

Driven Gear	Number of Teeth ( $N$ )	Rotational Speed ( $S$ , rpm)
Gear 1	8	270
Gear 2	12	180
Gear 3	16	135
Gear 4	18	?

Given that the rotational speed of the driven gear is inversely proportional to its number of teeth, what is the rotational speed, in rpm, of Gear 4?

Cevap: 120 rpm

Cevap

The rotational speed of Gear 4 is 120 rpm.

Since rotational speed is inversely proportional to the number of teeth, the product of these two values must remain constant. For all measured gears,

S \times N = 2160

. Dividing this constant by the 18 teeth of Gear 4 yields a rotational speed of 120 rpm.

Adım Adım Çözüm

Determine the proportionality constant

Constant

k = 2160

Because rotational speed (

S

) and number of teeth (

N

) are inversely proportional, their product is constant (

S \times N = k

). Using Gear 2 data,

12 \times 180 = 2160

Calculate the speed for Gear 4

Rotational speed = 120

Using the constant

k = 2160

and the number of teeth for Gear 4 (

N = 18

), the speed is calculated as

S = \frac{2160}{18} = 120

Anahtar Kavram

Direct and Inverse Proportionality

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

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