Question

3. A uniform semicircle with a radius of 2.00 cm is placed, flat edge down, on a horizontal removable platform. A pin is put in the left bottom corner to act as a pivot point and origin.

(a) What is the x − y location of the center of mass?

(b) What is the moment of inertia of the semicircle?

(c) The platform is suddenly removed. Draw a free-body diagram of the semicircle, with axes and ± directions.

(d) Using conservation of energy, what is the angular speed of the semicircle when the center of mass is directly below the pivot? (Be careful! The center of mass does not start at Ug=0.)

(e) If you instead used the rotational work equation to solve this problem, where are you likely to make a mistake?

Answer 1