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1. (a) Consider a rigid body pivoted at point O that is a distance $d$ from the center of mass as shown in the Figure below. The gravitational force provides a torque about an axis through O. Use the rotational form of Newton's second law, to prove that the equation of motion is $I \frac{d^2\theta}{dt^2} = -mgd\theta$ (b) What is the angular frequency $\omega$ of oscillation in terms of $m$, $I$, $g$ and $d$? (c) A physical pendulum in the form of a planar object moves in simple harmonic motion with a frequency of 0.500 Hz. The pendulum has a mass of 2.25 kg, and the pivot is located 0.450 m from the center of mass. Determine the moment of inertia of the pendulum about the pivot point. [7 points]

          1. (a) Consider a rigid body pivoted at point O that is a distance $d$ from the center of mass as shown in the Figure below. The gravitational force provides a torque about an axis through O. Use the rotational form of Newton's second law, to prove that the equation of motion is
$I \frac{d^2\theta}{dt^2} = -mgd\theta$
(b) What is the angular frequency $\omega$ of oscillation in terms of $m$, $I$, $g$ and $d$?
(c) A physical pendulum in the form of a planar object moves in simple harmonic motion with a frequency of 0.500 Hz. The pendulum has a mass of 2.25 kg, and the pivot is located 0.450 m from the center of mass. Determine the moment of inertia of the pendulum about the pivot point. [7 points]

1 a consider a rigid body pivoted at point o that is a distance d from the center of mass as shown in the figure below the gravitational force provides a torque about an axis through o use t 55402

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