Question

a 200 gm object is rotating with a constant linear speed of 2m/s. if the radius of rotation is 0.5 m, find angular velocity and the radial acceleration. if the speed increases to 4m/s in 10 sec, find the angular acceleration. Also find the net linear acceleration when is speed is 4m/s

Answer 1

angular velocity w = V/r
V is the linear speed and r is radius of circle
w = 2/0.5 = 4 rad/sec

Angular speed after 10 sec = 4/0.5 = 8 rad/sec
Angular acceleration, = change in angular speed / time
                                       = (8 - 4) /10 = 0.4 rad/sec²

Radial acceleration a_r = w² r = 8² * 0.5 = 32 m/sec²
tangential acceleration a_t = r = 0.4*0.5 = 0.2 m/sec²
Net linear acceleration =
                                     32 m/sec²