Question

The rotation of the smaller wheel in the figure causes the larger wheel to rotate. Find the radius of the largerwheel in the figure if the smaller wheel rotates 70.0° when the larger wheel rotates 40.0°The radius of the large wheel is approximately ____ cm.

Answer 1

Let's begin by listing out the information given to us:

r (1) = 11.4 cm, θ (1) = 70°, θ (2) = 40°, r(2) = ?

The arc length is the same for the 2 circles

r (1) * θ (1) = r (2) * θ (2)

11.4 * 70° = r (2) * 40°

r (2) = 11.4 * 70 ÷ 40

r (2) = 19.95 cm

Hence, the radius of the larger circle is 19.95 cm