9.39. Consider a thin sheet of mass M in the shape of an equilateral triangle with...

 

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9.39. Consider a thin sheet of mass M in the shape of an equilateral triangle with each side of length L. Find the moment of inertia about an axis passing through the vertex and perpendicular to the sheet. If this behaves as a physical pendulum, find the period for small oscillations. 9.40. Consider a homogeneous hemisphere of mass M and radius R. With its flat face up, it rests on a perfectly rough horizontal surface. Find the expression for the length of an equivalent simple pen- dulum for small oscillations about the equilibrium position. Let the radius of gyration about the horizontal axis passing through the center of mass be k- Lanath I and mass M. The system is 9.39. Consider a thin sheet of mass M in the shape of an equilateral triangle with each side of length L. Find the moment of inertia about an axis passing through the vertex and perpendicular to the sheet. If this behaves as a physical pendulum, find the period for small oscillations. 9.40. Consider a homogeneous hemisphere of mass M and radius R. With its flat face up, it rests on a perfectly rough horizontal surface. Find the expression for the length of an equivalent simple pen- dulum for small oscillations about the equilibrium position. Let the radius of gyration about the horizontal axis passing through the center of mass be k- Lanath I and mass M. The system is