A.) Calculate the moment of inertia I about
the pivot point.
Answer in units of kg Â· m2.

B.) The âtorqueâ equation of motion forsimple k = kappa
harmonic motion is of the form Ï = -kÎ¸
When the rod is displaced by a small angle
from the horizontal and released, calculate
kappa. Assume Î¸ is so small that the small angle
approximation may be used.
Answer in units of N Â· m.

C.) Calculate the angular velocity of the resulting
simple harmonic motion.
Answer in units of rad/s.

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a) At the bottom is a 3 step pulley; consisting ofthree wheelsof different diameters.b) The rotating arm has two massesattached,and is screwed into the 3 step pulley. Whenthe pulleyrotates, so does the rod.c) The string is wrapped around one ofthewheels in the 3 step pulley and passes overthe smart pulley. Themass hanger is hooked into the loop at the end of the string.d)When the system is released, the mass hanger falls, turning thesmart pulley, and the 3 step pulley withthe rod attached. e)Assume: that the smart pulley is very light, so its moment ofinertia is negligible as compared to the moment of inertia of the 3step pulley and rod.

Suppose that you measured the moment of inertia of the system as I= 5.05 kg-m2. Assume the diameter of the pulley around which youwrap the string is d = 2.5 cm.

a) Suppose the system is initially spinning at angular speed Ïo =9.27 rad/s. After you drop a disk of mass 856 g on it, the systemrotates at Ïf = 8.35 rad/s. Find:
- the moment of inertia of the disk: kg-m2
- the radius of the disk: cm

b) suppose the system is initially spinning at angular speed Ïo =2.05 rad/s. After you drop a cube of mass 786 g on it, the systemrotates at Ïf = 1.79 rad/s. Find:
- the moment of inertia of the cube: kg-m2
- the length of one side of the cube: cm

14.87 .. CALC A slender, uniform, metal rod with mass M is pivoted without friction about an axis through its midpoint and perpendicular to the rod. A horizontal spring with force con- stant k is attached to the lower end of the rod, with the other end Figure P14.87 of the spring attached to a rigid support. If the rod is displaced by a small angle from the vertical (Fig. P14.87) and released, show that it moves in angular SHM and calculate the period. (Hint: Assume that the angle is small enough for the approximations [ sin Ꮎ = Ꮎ and cos Ꮎ = 1 to be valid. The motion is simple har- monic if d-0/dt = -0-0, and the period is then T = 27/0.)

a)when you drop the mass holder, the system rotates at angularacceleration Î±. If you wrapped thestring around a larger diameter pulley and dropped the mass holder,the acceleration of the system would be:

exactlyÎ±? less than a? more than a?

Suppose that you measured themoment of inertia of the system as I = 5.05 kg-m². Assume the diameterof the pulley around which you wrap the string is d =2.5 cm.

a) In trial 1:the system is initially spinning at angular speedÏ_o = 9.27 rad/s. After you drop a disk of mass856 g on it, the system rotatesat Ï_f = 8.35 rad/s. Find:
- the moment of inertia of thedisk: kg-m²
- the radius of the disk: cm

b) In trial 3: suppose the system is initially spinning at angularspeed Ï_o = 2.05 rad/s. After you drop a cube of mass786 g on it, the system rotatesat Ï_f = 1.79 rad/s. Find:
- the moment of inertia of thecube: kg-m²
- the length of one side of the cube: cm

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