A uniform rod of mass M = 2 kg and length L = 1.5 m is attached to a wall with a frictionless pivot and a string as shown in the diagram above. The initial angle of the rod with respect to the wall, is = 39º. The string is then cut. The moment of inertia of a rod about an axis through one end is 1/3ML². What is the angular acceleration of the rod, a, immediately after the string is cut? A: a = 6.17 rad/s² What is the angular velocity w of the rod when it is horizontal (0 = 90°)? A: w 3.9 rad/sec 0 ΔΕ(m) = 0 T net, P = la 2 2 Iw₁² + MgYcm1 = Iw² + MgYcm0

a top with radius 10cm, mass 2 kg has a string around the edge and is initially at rest. assume the top can be reasonably approximated as a solid cylinder. the top is held in place as the string is pulled. the string applies a force of 10N tangential to the edge for 2s. what is the angular velocity (in radians per second) of the top after 3 seconds? what is the angular momentum of the top after the string is pulled? after the string is pulled, the top is released. it travels away from its initial position at a linear velocity of 10m/s. what is the rotational velocity (in radians per s) at this top? assume no friction

A yo-yo is made of two uniform disks, each of mass M and radius R, which are glued to a smaller central axle of negligible mass and radius 0.5R (see figure). A string is wrapped tightly around the axle. The yo-yo is then released from rest and allowed to drop downwards, as the string unwinds without slipping from the central axle.  Part (a)  Find the moment of inertia, I, of the yo-yo with respect to an axis through the common centers of the disks, in terms of the mass and radius.   Part (b)  Find the linear speed V of the yo-yo, after it has descended a distance H. Part (c)  Calculate the magnitude of the linear velocity V, in meters per second, of the yo-yo after it has fallen a distance 0.39 m

Four particles, each of mass 0.39 kg, are placed at the vertices of a square with sides of length 0.57 m. The particles are connected by rods of negligible mass. This rigid body can rotate in a vertical plane about a horizontal axis A that passes through one of the particles. The body is released from rest with rod AB horizontal, as shown in the figure. (a) What is the rotational inertia of the body about axis A? (b) What is the angular speed of the body about axis A at the instant rod AB swings through the vertical position? Rotation аxis A B (a) Number i Units (b) Number i Units

A spool consists of a cylinder with two circular disks glued on either end. It has mass m, moment of inertia I, inner (cylinder) radius r, and outer (disk) radius R. String is wrapped tightly around the cylinder. The spool is placed on its side and the string is pulled with force T from an angle 0 above the horizontal. The spool rolls without slipping. (a) Compute the angular acceleration about the center of mass at the instant the force is first applied. (b) Which way does the spool roll, right or left? Does this depend on the properties of the spool and/or the angle 0? If so, find a formula. Note: if you did not succeed in part 1, you can still get partial credit here for a correct qualitative discussion.

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 wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius r = 0.156 m and mass 4.32 kg, and two thin crossed rods of mass 7.80 kg each. A farmer would like to replace his wheels with uniform disks = 0.0525 m thick, made out of a material with a density of 5990 kg per cubic meter. If the new wheel is to have the same ta %3D moment of inertia about its center as the old wheel about its center, what should the radius of the disk be? = PA rd

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.

The uniform thin rod in the figure below has mass M = 2.50 kg and length L = 2.87 m and is free to rotate on a frictionless pin. At the instant the rod is released from rest in the horizontal position, find the magnitude of the rod's angular acceleration, the tangential acceleration of the rod's center of mass, and the tangential acceleration of the rod's free end. HINT L/2 × CG M O (a) the rod's angular acceleration (in rad/s²) rad/s² (b) the tangential acceleration of the rod's center of mass (in m/s²) (c) m/s² the tangential acceleration of the rod's free end (in m/s²) m/s²