Question 1096677
The distance between the centers is the sum of the radii, So, the radius of the larger gear is
21 inches - 9 inches = 12 inches.
The angle in radians is the length of the arc divided by the radius,
so the length of the arc is the radius times the measure of the angle in radians.
During 1 second, the smaller gear turns 3 radians,
meaning that the point of contact with the larger gear moves along an arc of length
{{{3*(9in)=27in}}} on the edge of the small gear.
For the large gear, unless the gears are slipping, the point of contract .must have moved the same distance.
However, it moved along an arc of a circle of radius = 12 inches.
The measure of the angle in radians is
{{{27in/"12 in"=highlight(9/4=2.25)}}} .