A diver leaves the platform with her body straight. Her body is in a relatively slow rotation, with an angular speed of 4.0 rad/s. She then tucks into a pike position, with her body essentially folded in half. We can use a simple model to understand what happens next. First, model her 50 kg, 1.8 m body as uniform. Next, assume that when she goes into a pike position, she really does fold her body exactly in half. In terms of this model, a. What is her initial moment of inertia?b. What is her moment of inertia in the pike position?c. What is her angular speed in the pike position?d. How many rotations does she complete in the 1.3 s that she holds the pike position?

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PLEASE DRAW AN FBD AND ANSWER IT ON A PAPER   The figure shown is on a fixed frictionless axle. It has a moment of inertia of I = 50 kg-m2 . The forces acting on the object are F1 = 100 N, F2 = 200 N, and F3 = 250 N acting at different radii R1 =60 cm, R2 = 42 cm, and R3 = 28 cm. Determine the angular acceleration of the object.

Modern wind turbines generate electricity from wind power. The large, massive blades have a large moment of inertia and carry a great amount of angular momentum when rotating. A wind turbine has a total of 3 blades. Each blade has a mass of m = 5500 kg distributed uniformly along its length and extends a distance r = 44 m from the center of rotation. The turbine rotates with a frequency of f = 12 rpm. a)Calculate the total moment of inertia of the wind turbine about its axis, in units of kilogram meters squared.  b)Enter an expression for the angular momentum of the wind turbine, in terms of the defined quantities.  c)Calculate the angular momentum of the wind turbine, in units of kilogram meters squared per second.

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The outstretched hands and arms of a figure skater preparing for a spin can be considered a slender rod pivoting about an axis through its center (Figure 1). When his hands and arms are brought in and wrapped around his body to execute the spin, the hands and arms can be considered a thin-walled hollow cylinder. His hands and arms have a combined mass 8.0 kg. When outstretched, they span 1.6 m ; when wrapped, they form a thin-walled hollow cylinder of radius 26 cm. The moment of inertia about the rotation axis of the remainder of his body is constant and equal to 0.4 kg⋅m2. If his original angular speed is 0.30 rev/s, what is his final angular speed?

A disk initially at rest is fixed to a vertical axis of rotation and a 40 kg child is standing on the disk initially at rest 0.5 meters away from the axis of rotation. The rotational inertia of the disk is 50 kgm2. The boy pushes and jumps off the disk and the disk begins to rotate at 0.5 rad/s. Calculate the linear velocity of the child as they push off the disk. (The rotational inertia of the boy is mr2)

A solid, uniform disk of radius 0.250 m and mass 49.0 kg rolls down a ramp of length 3.80 m that makes an angle of 12.0° with the horizontal. The disk starts from rest from the top of the ramp. (a) Find the speed of the disk's center of mass when it reaches the bottom of the ramp. m/s (b) Find the angular speed of the disk at the bottom of the ramp. rad/s

A vinyl record spins freely on a frinctionless turntable.  The mass of the record is 0.10 kg, the radius is 0.10 m, the rotational inertia is 5.0 x 10-4 kgm2 and it rotates with angular speed of 4.7 rad/s.  A 0.024 kg piece of clay falls on the edge of the record.  Determine the angular speed of the record right after the clay sticks to it. Use conservation of momentum.

Hi please help: a solid disk of radius R= 70 cm rotates about its center at an angular speed of 43 revolutions per minute. The mass of the disk is M= 7.7 kg. The moment of inertia of a solid disk is given by 1/2 MR^2. What is the rotational kinetic energy (in Joules) of the disk? Answer with three significant figures