Question

No vector method pls

1. The circular disk rotates about its center O. At a certain instant point A has a velocity v,-0.8ms in the direction shown, and at the same instant the tangent of the angle θ made by the total acceleration vector of any point B with its radial line to O is 0.6. For this instant compute the angular acceleration of the disk. 100 mm

Answer 1

Angular velocity of the disk, w = V_A/r w = 0.8 m/s/100m times 1000 = 8 rad/s at point B tangent of theta made by total accl vector is 0.6 i e tan theta = alpha_t (tangential component)/alpha_n (normal component) So, alpha_t/alpha_n = 0.6 We also know that alpha_n = w^2 r = S^2 times 100/1000 m/s^2 = 6.4 m/s^2 Hence, alpha_t = (0.6 times 6.4)m/s^2 = 3.84 m/s^2 Now, alpha_t = alpha r where, alpha = angular accl of the disk or alpha = alpha_t/r = 3.84 m/s^2/100/1000 m = 38.4 rad/s^2