Rolling motion of an unbalanced disk

[NoYou]

Homework Statement

The mass center G of a 5kg wheel of radius R = 300 mm is located at a distance r = 100 mm from its geometric center C. The centroidal radius of gyration is k = 150 mm. As the wheel rolls without sliding, its angular velocity varies and it is observed that it is = 8 rad/s in position shown. Determine the corresponding angular acceleration of the wheel.

Homework Equations

Ac=Ag=Ac + Ag/c = Ac + (Ag/c)tangent + (Ag/c) Normal
I= mk^2
a=r$$\alpha$$

The Attempt at a Solution

 

[member 553083]

I= 5 kg(150mm)^2 = 1125 kg m^2a=r\alpha = 100 mm (8 rad/s) = 800 rad/s^2Ac = Ag = I \alpha = (1125 kg m^2)(8 rad/s) = 9000 rad/s^2Ag = Ac + (Ag/c) tangent + (Ag/c) Normal = 9000 rad/s^2 + (Ag/300mm)Tangent + (Ag/300mm)NormalAg = 9000 rad/s^2 + (Ag/300mm)(cos30) + (Ag/300mm)(sin30) = 9000 rad/s^2 + (Ag/3)Ag = 9000 rad/s^2 + 3000 rad/s^2 = 12000 rad/s^2 Therefore, the angular acceleration of the wheel is 12000 rad/s^2