a. A point on the rim of a disk rotating at constant angular velocity has no tangential acceleration. b. The point on the rim now has both radial and tangential acceleration. c. In case (a), linear acceleration will not change. In case (b), the tangential acceleration stays constant and the magnitude of the radial component of acceleration will increase as linear speed also increases.
Work Step by Step
a. The tangential speed is constant. The point does have radial, i.e., centripetal, acceleration. The point’s velocity is changing, because the velocity vector is changing direction. b. Now let the disk’s angular velocity increase uniformly. The point on the rim now has both radial and tangential acceleration. It is speeding up (tangential acceleration) and its velocity is continuously changing direction (radial acceleration). c. In the case of constant angular speed, neither component of linear acceleration will change. In the case of angular velocity increasing uniformly, the magnitude of the radial component of acceleration will increase as the linear speed increases. The tangential acceleration stays constant.