Question

Two gears are adjusted so that the smaller gear drives the larger one. if the smaller gear of 3.7cm rotates through an angle of 300° through how many degrees does the larger gear of 7.1cm rotate
please help me

Answer 1

Answer:

The larger gear will rotate through 156°

Step-by-step explanation:

Arc Length

The arc length S of an angle θ on a circle of radius r is:

$S = \theta r$

Where θ is expressed in radians.

The smaller gear of r1=3.7 cm drives a larger gear of r2=7.1 cm. The smaller gear rotates through an angle of θ1=300°.

Convert the angle to radians:

$\displaystyle \theta_1=300*\frac{\pi}{180}=\frac{5\pi}{3}$

The arc length of the smaller gear is:

$\displaystyle S_1=\frac{5\pi}{3}\cdot 3.7$

$\displaystyle S_1=\frac{18.5\pi}{3}$

The larger gear rotates the same arc length, so:

$\displaystyle S_2=\frac{18.5\pi}{3}$

$\displaystyle \theta_2\cdot r_2=\frac{18.5\pi}{3}$

Solving for θ2:

$\displaystyle \theta_2=\frac{18.5\pi}{3r_2}$

$\displaystyle \theta_2=\frac{18.5\pi}{3*7.1}$

$\theta_2=2.73\ radians$

$\displaystyle \theta_2=2.73*\frac{180}{\pi}=156$

The larger gear will rotate through 156°