Question

A gear of radius 7.2 cm turns at 11 revolutions per second. What is the linear velocity of the gear in meters per second?

Answer 1

Linear velocity is given by the formula v = ωr, where ω is the angular velocity in radians, and r is the radius.

We first solve for ω:
11 revs/sec = (11 revs/sec) x (2πrad/rev) = 22π rad/sec.
(note: 2πrad/rev means that there are 2π radians in one revolution)

v = ωr; where v is in meters per second
v = (22π rad/s)(7.2 cm)(10⁻² m/1 cm) = 4.976 m/s