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.

Answer 1

yer assuming no slipping

if so, you can say that \(4 \theta_4 = 7 \theta _7\)

that is, the distance travelled by a point on the rim of each gear must be the same, cos there is no slippage

tbc, \(\theta_4\) is the angle the 4 inch wheel turns through and \(\theta_7\) is the angle the 7 inch wheel turns through

so you plug the numbers in

Answer 2

"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?"

So \(\theta_4 = 360\)

\(\implies 4 \times 360 = 7 \theta _7 \implies \theta_7 = \dfrac{ 4 \times 360}{7}\)

that's a job for yer calculator :)

Answer 3

Jaysus, delete-fest :)

Answer 4

ikr ._.