lum that.consists of two uniform rl nd mass 2.50 kg, and the second r kg. Both rings are attached to a ro s freely about frictionless pivot o. I s for small oscillations, what must Show that the moment of inertia for a disk w MR2 xis is giving by:

A physical pendulum is constructed such that two spheres of different radii are welded together.  A rod is then welded to the top of these two spheres as shown.  The length of the rod is 2.90 m while the mass is 2.00 kg.  The radius of the small (upper) sphere is 0.790 m with a mass of 8.20 kg.  The radius of the lower (larger) sphere is 0.960 m with a mass of 11.6 kg.  The entire system is hung from the end of the rod.   a. what is the rotational intertia of the rod?   b. what is the rotational intertial of the small sphere?   c. what is the rotational intertia of the large sphere?   d. what is the distance from the pivot point to the center of mass of the system?   e. what is the period of oscillation of the pendulum?

You have made a physical pendulum by swinging a rod of mass M = 1.08 kg and length L = 1.45 meters around its end. The mass of the rod is distributed uniformly along its length. We will assume that the amplitude of the swing is max = 19.34 degrees. Solid Rod Swings in Simple Harmonic Motion ^ 0=-0, max 0=+0₁ max Determine all the following: The FORMULA for the moment of inertia of your rod, I = The distance from the pivot point to the Center-Of-Mass, d = The angular frequency of the pendulum, w = The amplitude of the motion in radians, max = radians The angular velocity when 0 = 64% of full swing, w(0 = 0.64 0max): NOTE: The first question requires a FORMULA, not a value. rad/sec = meters rad/sec

A physical pendulum composed of a solid sphere with radius R = 0.500m, is hanged from a ceiling by string of length equal to radius. What are the (a) angular frequency, (b) period, (c) frequency of the system for small angles of oscillation? The moment of inertia of the pendulum about its axis of rotation is I= 2/5 mR^2