Question

Two gears are adjusted so that the smaller gear drives the larger one. The radius of the smaller gear is 3.7 cm and the radius of the larger gear is 7.1 cm.
If the smaller gear rotates through an angle of 300°, through how many degrees does the larger gear rotate?

Answer 1

Answer:

$\theta=156^0$

Step-by-step explanation:

The smaller gear rotates through an angle of 300°.

In radian, 300°= $300X\frac{\pi}{180} =\frac{5\pi}{3}$

The arc length, s on the smaller gear(with a radius of 3.7 cm) is:

$s=r\theta$

$s= \frac{5\pi}{3} X 3.7=\frac{18.5\pi}{3}$

The larger gear moves through the same arc length.

Therefore:

Arc length of the larger gear, $s=\frac{18.5\pi}{3}$

Radius of the larger gear =7.1cm

$s=r\theta$

$\frac{18.5\pi}{3}=7.1\theta\\\theta=\frac{18.5\pi}{3X7.1}\\\theta=\frac{18.5\pi}{21.3}$

To convert back to degrees

$\theta=\frac{18.5\pi}{21.3}\\\theta=\frac{18.5\pi}{21.3}X\frac{180}{\pi} =156.33\\\\\theta=156^0$

The larger gear rotates through an angle of 156 degrees.