A uniform thin rod of mass M = 3.37 kg pivots about an axis through its center and perpendicular to its length. Two small bodies, each of mass m = 0.219 kg, are attached to the ends of the rod. What must the length L of the rod be so that the moment of inertia of the three-body system with respect to the described axis is I = 0.975 kg-m² ? L = m m m L

Multiple-Concept Example 10 reviews the approach and some of the concepts that are pertinent to this problem. The figure shows a model for the motion of the human forearm in throwing a dart. Because of the force M applied by the triceps muscle, the forearm can rotate about an axis at the elbow joint. Assume that the forearm has the dimensions shown in the figure and a moment of inertia of 0.077 kg-m2 (including the effect of the dart) relative to the axis at the elbow. Assume also that the force M acts perpendicular to the forearm. Ignoring the effect of gravity and any frictional forces, determine the magnitude of the force M needed to give the dart a tangential speed of 3.1 m/s in 0.13 s, starting from rest. 0.28 m Axis at elbow joint 0.025 m Number i Units

A yoyo is constructed by attaching three uniform, solid disks along their central axes as shown. The two outer disks are identical, each with mass M= 51 g, radius R= 3.9 AF cm, and moment of inertia 1/2MR². The central, smaller disk has mass M/2 and radius R/2. A light, flexible string of negligible mass is wrapped counterclockwise around the central disk of the The yoyo is then placed on a horizontal tabletop and the string is gently pulled with a constant force F = 0.25 N. The tension in the string is not sufficient to cause the yoyo to leave the tabletop. In this problem consider the two cases show. In Case 1 the string is pulled straight up, perpendicular to the tabletop. In Case 2 the string is pulled horizontally, parallel to the tabletop. In both cases the yoyo rolls without slipping. yoyo. Case 1: I F Case 2: Part (a) What is the moment of inertia ICM about the central axis (i.e. the axis perpendicular to the circular face) of the yoyo, in kg•m². ICM= 8.242 * 10(- 5 ) ICM=…

A solid disk rotates in the horizontal plane at an angular velocity of 0.042 rad/s with respect to an axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.089 kg·m2. From above, sand is dropped straight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance 0.29 m from the axis. The sand in the ring has a mass of 0.42 kg. After all the sand is in place, what is the angular velocity of the disk?

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.

The axis of rotation of a thin plate is located at the left side, as shown in the figure. Calculate the moment of inertia I if the plate has a length L of 7.00 cm, a width W of 5.00 cm, and a uniform mass density of 3.25 g/cm2.

A disk of radius R and thickness t has a mass density that increases from the center outward, given by p = po (r/R), where r is the distance from the axis of the disk. What is the moment of inertia about the disk axis in terms of M and R? O MR 2MR O sMP 3MR 5 O 2MR 3 5MR 3

A small pine tree has a mass of 19 kg. Its center of mass is located at 0.87 m from the ground. Its trunk is sawed though at ground level, causing the tree to fall, with the severed trunk acting as the pivot point. At the instant the falling tree makes a 16° angle with the vertical, the angular acceleration of the tree is 2.6 rad/s. What is the moment of inertia of the tree?

Everyone's favorite flying sport disk can be approximated as the combination of a thin outer hoop and a uniform disk, both of diameter Da = 0.273 m. The mass of the hoop part is mh = : 0.120 kg and the mass of the disk part is md = 0.050 kg. Imagine making a boomerang that has the same total moment of inertia around its center as the sport disk. The boomerang is to be constructed in the shape of an "X," which can be approximated as two thin, uniform rods joined at their midpoints. If the total mass of the boomerang is to be m₁ = 0.235 kg, what must be the length Lы of the boomerang? | I Lb = = Cross-sectional view m