What’s the linear speed?

Question

A hamster wheel of radius 3 inches spins at 4 revolutions per second. What’s the wheels linear speed?

Answer 1

a point on the wheel making 1 revolution covers the distance of the wheel's circumference. The circumference is 2*pi*r, where r is the radius = 3 inches. Thus, the point on the wheel making one revolution will travel ~ 2*6*3.14159 = 18,85 inches.

Four revolutions is equal to 4*18.85 ~ 75.4 inches. Since the wheel turns at 4 revolutions/second, the linear speed is about 75.4 in/sec.

Answer 2

The angular velocity is (4 revolutions/sec)•(2π radians/revolution) = 8π radians/sec. The linear speed is the tangential speed at the outer rim and is the angular velocity times the radius or (8π radians/sec)•(3 inches) = 24π inches/sec ≈ 75 inches/sec