A uniform circular disc of mass 1.5kg and radius 0.5m is initially at rest on a horizontal frictionless surface. Three forces of equal magnitude F=0.5N are applied simultaneously along the three sides of an equilateral triangle XYZ with its vertices on the perimeter of the disc (see figure). One second after applying the forces, the angular speed of the disc in rads−1 is
Answer: 2
Solution
Each force produces a torque about the center. For a force tangent to the circle at angle, the perpendicular distance is rsin30∘=0.5×0.5=0.25 m.
Net torque: τ=3Frsin30∘=3×0.5×0.5×0.5=0.375 N·m.
Moment of inertia: I=21mr2=21×1.5×0.52=0.1875 kg·m².