One gear wheel turns another the teeth being on the rims The

One gear wheel turns another the teeth being on the rims. The wheels have 10-cm and 30-cm radii, and the smaller wheel rotates at 20 rpm. Find the angular speed of the larger wheel in radians per second. The angular speed of the larger wheel is radians/sec (Simplify your answer. Type an integer or decimal rounded to three decimal place as needed)

Solution

Small Gear Circumference = 2 (pi) r = 2 (pi) (10 cm) = 20 pi cm
Small Gear Angular Speed = [2 (pi) radians / revolution] [20 revolutions / minute] [1 minute / 60 seconds] = (2/3) (pi) radians / second
Large Gear Circumference = 2 (pi) r = 2 (pi) (30 cm) = 60 pi cm

Large Gear Angular Speed = [Small Gear Angular Speed] [Small Gear Circumference] / [Large Gear Circumference] = [(2/3) (pi) radians / second] [20 pi cm] / [60 pi cm] = (2/9)(pi) radians / second
= 0.698 rad/s approximately