Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

We can find the speed of the string after 1.0 meter of string has been unwound; $v^2 = v_0^2+2ax = 0 +2ax$ $v =\sqrt{2ax} = \sqrt{(2)(1.5~m/s^2)(1.0~m)}$ $v = 1.73~m/s$ We can find the angular speed; $\omega = \frac{v}{r} = \frac{1.73~m/s}{0.030~m}$ $\omega = 57.7~rad/s$ We can express the angular speed in units of rpm; $\omega = (57.7~rad/s)(\frac{60~s}{1~min})(\frac{1~rev}{2\pi~rad})$ $\omega = 551~rpm$ The angular speed is 551 rpm.