Question

A large metal disk with mass M=5 kg and R= 3m starts from rest and is free to without friction about an axis passing through its center of mass point 0. perpendicular to the disk. 4 light engines providing a constant thrust force F=20 N, are connected to the circumforce of the disk in the orientation shown. dashed lines are tangent to the disk. Engines ignite at t=0. The moment of inertia of the disk about its center I disk= (MR^2)/2

a) F net generate by the 4 engines.

b) Angular acceleration

c) Angular velocity and rotational kinetic energy of the disk at t=4 s

d) The magnitude of the total acceleration vector 'a' of a point A on the disk located at x distance 1.50 m from the center of the disk at t= 4 s

Answer 1

Calculate F net generate by the 4 engines. Fnet = 4 x F, = 4x(20) = 80 N Calculate the angular acceleration using the net torque equation. =la MR? FXR= 2 12 a Ft MR 2 a a= 2F 2(80) =10.67 rad/s? MR (5)(3) Calculate the angular velocity of the disk at t=4 s. m = 0, +at = 0+(10.67)(4) = 42.68 rad/s Calculate the rotational kinetic energy of the disk at t=4 s. 1 MR? 1 (5)(3) K; 2 2 2 2 -- 10 = u( 4 12 = 063)* }(42.689 = 204928 ) Calculate the magnitude of the total acceleration vector 'a' of a point A. an= pa, +a? = R62)* +(Ra)* =R@)*+(a)? = (1-5)(42.68)* +(10.67) = 2732.42 m/s?