Problem 1a: A uniform circular disk of mass 1.5 kg and radius 0.5 m is initially at rest on a horizontal surface. Three constant forces of equal magnitude, F = 0.5 N are applied simultaneously at t = 0 along the three sides of an equilateral triangle XYZ with its vertices on the perimeter of the disk (see figure below). Find the angular speed of the disk in rad/s at t = 1 second. (I_G)_disk = 0.5 MR². Ignore friction for calculation purpose.

Problem 1b: Consider the homogeneous sphere of diameter D pivoted about point O. Find the distance "a" (in terms of D) where the horizontal force F must be applied such that the horizontal component of the reaction at the point of suspension is zero. (I_G)_sphere = 2MR²/5;

Problem 2: The 50 kg (l = 1 m) slender bar is pressed against a spring (k = 30 kN/m) compressing it x = 11 cm and then released from rest from a horizontal position as shown in the figure below. Determine

a) The angular speed of the bar when it makes 0 = 45° with the horizontal and

b) The largest angle attained by the bar. (I_G)_bar = ML²/12; (I_o)_bar =  ML²/3;

Problem 3: Consider a homogeneous sphere of mass m and radius r that rolls without slip inside a circular surface of radius R. The coefficient of kinetic friction for the surface is µ_k = 0.4. The sphere is released from rest at A where it makes angle ß with the vertical. Find the magnitude of normal force acting on the sphere as it passes point B. (I_G)_Sphere = 2mr²/5.