What is the angular acceleration of the pencil when it makes an angle of 10.0 degrees with the vertical?

R:  If they give you the net torque and the moment of inertia already, it's pretty easy. 

torque = I * alpha, where I is moment of inertia, alpha is angular acceleration. 

Thus, 0.098 / 0.000075 = 1306.666... rad / s^2 

The angular acceleration remains constant, but the angular velocity at that point (if you want it) is 21.36 rad / s