Question

Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 4 inches, and the larger gear has a radius of 7 inches.

two circles touching at one point. Larger circle has radius of 7 inches. Smaller circle has radius of 4 inches.

Part 1: What is the angle measure, in degrees and rounded to the nearest tenth, through which the larger gear has rotated when the smaller gear has made one complete rotation?

Part 2: How many rotations will the smaller gear make during one complete rotation of the larger gear?

Answer 1

@phi
@myininaya
@ganeshie8
@mathmath333

Answer 2

can someone help pls

Answer 3

I would find the circumference of each circle as a first step.

Answer 4

ok

Answer 5

let r1 be radius for small circle
and let r2 be radius for small circle
therefore length of arc S
\(\large\tt \begin{align} \color{black}{s_1=r_1\theta_1\\~\\
s_2=r_2\theta_2\\~\\
}\end{align}\)
u have find \(\large\tt \begin{align} \color{black}{\theta_2
}\end{align}\)when \(\large\tt \begin{align} \color{black}{\theta_1
=2\pi\\~\\
}\end{align}\)
\(\large\tt \begin{align} \color{black}{s_1=r_1\theta_1\\~\\
s_1=4(2\pi)\\~\\
}\end{align}\)
u have to find the angle through which the larger
gear has rotated when the smaller gear has
made one complete rotation.
\(\large\tt \begin{align} \color{black}{thus~~s_1=s_2\\~\\
s_2=r_2\theta_2\\
8\pi=7\theta_2\\
\theta_2=\dfrac{8\times 180}{7}\\
=205~~ degrees~~
}\end{align}\)

Answer 6

ok thx