Question

The platform shown below rotates at constant rate of 6 rad/s. The block moves outward with a speed (r,dot) that varies with respect to time. If the block starts from rest at the center of the platform, determine the magnitude of its acceleration (in meters/second^2) when t = 1 second.

Please use four significant figures in the final answer. Thank you!

The platform shown below rotates at constant rate of 6 rad/s. The block moves outward with a speed (r,dot) that varies with respect to time. If the block starts from rest at the center of the platform, determine the magnitude of its acceleration (in %) when t = 1 second. r = (4t)m/s 0 = 6 rad/s r e

Answer 1

Centripetal acceleration acts towards the center of rotation

Forz 4t m/s s = 44 ml. rad Block starts from centre. 6 = 6 ead/s 0 v=4tml de = 4 m/s word a At tal secondo Ve= ctmls ae=4m/s2 Distance travelled along the radial direction in 1 second ell! = 4t dt at² = 2m. O 0 U Vo = n. 8 = 2x6 m/s = 12 m/s. Net acceleration 마 a = 4 m/s va Grac E 4 - 144 2 =-68 m m/s (-ve radial direction)

a_{​​​​​​c} = 72 m/s^{​​​​​​2} radially inward.

Net acceleration = 4- 72 =-68 m/s2