The 4.0 m long bar shown in the figure is fixed so that it can rotate freely around point O at the end of the bar. Three forces are applied along the bar at the positions and angles shown. Use the convention that a counter-clockwise spin is positive. If the bar has a mass of 12 kg, what is its moment of inertia? 27 N 16 N 30 +3.0 m→ 45° - 4.0 m- 33 N 48 kgm2 O 192 kgm2 O 64 kgm2 O 16 kgm2

If an object has a moment of inertia 37 kg-m2 and the magnitude of its rotational angular momentum is 88 kg · m2/s, what is its rotational kinetic energy? Krot =

In the figure below, a very light rope is wrapped around a wheel of radius R = 1.17 meters and does not slip. The wheel is mounted with frictionless bearings on an axle through its center. A block of mass M = 19.7 kg is suspended from the end of the rope. When the system is released from rest it is observed that the block descends 10.39 meters in 1.49 seconds. What is the N moment of inertia of the wheel?

A uniform thin rod of mass ?=3.47 kg pivots about an axis through its center and perpendicular to its length. Two small bodies, each of mass ?=0.277 kg, are attached to the ends of the rod. What must the length ? of the rod be so that the moment of inertia of the three-body system with respect to the described axis is ?=0.987 kg·m2 ?

Two uniform, solid spheres (one has a mass M and a radius R and the other has a mass M and a radius Rb=2R are connected by a thin, uniform rod of length L=2R and mass M. Note that the figure may not be to scale. Find an expression for the moment of inertia I about the axis through the center of the rod. Write the expression in terms of M, R, and a numerical factor in fraction form.

Calculate the moment of inertia of the object shown about an axis coming perpendicularly out of the paper, and passing through the leftmost mass. Give: M = 9 kg, L = 2 m, and the connecting rods are mass-less. Treat the masses as point masses.

When a diver gets into a tuck position by pulling in her arms and legs, she increases her angular speed. Before she goes into the tuck position, her angular velocity is 5.5 rad/s and she has a moment of inertia of 1.7 kg · m². Once she gets into the tuck position, her angular speed is 15.1 rad/s. Determine her moment of inertia when she is in the tuck position. Assume the net torque on her is zero. kg · m2

A pulley of moment of inertia 2.0kg−m^2 is mounted on a wall as shown in the following figure. Light strings are wrapped around two circumferences of the pulley and weights are attached. What is the angular acceleration of the pulley? Using the following values: r1 = 50 cm, r2 = 20 cm, m1 = 1kg, m2 = 2kg When I solved this I got -0.46 rad/ s^2. I kind of just want confirmation.

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.

A pulley with moment of inertia I = 0.75 kg-m² and radius R = 15 cm is mounted on a wall. A light string is wrapped around the pulley with a mass m = 2.0 kg attached to the end. The pulley rotates as the mass falls. Use Newton's second law to calculate the acceleration of the mass. Check that your formula gives the expected behavior when I →0. => To help get started, the free body diagrams m and the pulley is shown below. T m Write down Newton's second law for each diagram. Use (and explain) the relationship R a = RO TIL R T