Question

A tire of radius 1.5 ft rolls without slipping along a horizontal track with uniform angular acceleration of 3 rad/s^2 from rest.

(a) How long will it take the point on tire touching the track to acquire an angular frequency of 30 rad/s and how far horizontally could the tire travel at this instant?

(b) What was the tangential speed, centripetal acceleration, and tangential acceleration of the point on tire in part (a)?

Answer 1

(a) The time is

$$t=\frac \omega\alpha=10\text{ s}.$$

(b) At 30 rad/s, the tangential speed, centripetal acceleration, and tangential acceleration, are respectively:

$$v=\omega r=45\text{ ft/s}.\\\space\\ a_c=\omega^2r=1350\text{ ft/s}^2,\\\space\\ a_\tau=\alpha r=4.5\text{ ft/s}^2.$$