The apparatus shown above consists of two identical springs of negligible mass, each with spring constant k = 20.4 N/m and each attached at one end to a vertical rotating pole. Identical small spheres of mass m are attached to the other ends of the springs. The spheres are constrained by horizontal guides of negligible friction, each of which has a ruler below it for measuring the radial position r of the sphere. The system can be manually rotated about the pole’s axis. In a lab experiment, a student adjusts the rotational speed so that the spheres move to a desired radius r. For each such value of r, the student measures the rotational period T. The student’s partially completed data table is shown below. The length of each unstretched spring is L = 0.15 m. horizontal motion

A uniform rod is set up so that it can rotate about an axis at perpendicular to one of its ends. The length and mass of the rod are 0.765 m and 1.27 kg respectively. A force of constant magnitude ?F acts on the rod at the end opposite the rotation axis. The direction of the force is perpendicular to both the rod's length and the rotation axis. Calculate the value of ?F that will accelerate the rod from rest to an angular speed of 6.21 rad/s in 9.91 s

A string is wrapped around a disk of mass m = 2.2 kg and radius R = 0.08 m. Starting from rest, you pull the string with a constant force F = 9 N along a nearly frictionless surface. At the instant when the center of the disk has moved a distance x = 0.12 m, your hand has moved a distance of d = 0.27 m. m d (a) At this instant, what is the speed of the center of mass of the disk? Vcm = m/s (b) At this instant, how much rotational kinetic energy does the disk have relative to its center of mass? Krot = Additional Materials M eBook

A grindstone in the shape of a solid disk (mass M = 50.0 kg) and radius R = 0.200 m (moment of Inertia | = 1/2 MR^2) is rotating at 90.0 rad/s. You press a metal box against the rim with a force F = 180 N and the grindstone comes to rest in 10.0 s. There is a friction force between the grindstone and the box. Find the magnitude of the friction.

A potter's wheel having a radius 0.51 m and a moment of inertia of 14.9 kg · m2 is rotating freely at 50 rev/min. The potter can stop the wheel in 7.0 s by pressing a wet rag against the rim and exerting a radially inward force of 74 N. Find the effective coefficient of kinetic friction between the wheel and the wet rag.

A 250 g piece of kryptonite is attached to a 90 cm long masless string to form a pendulum. At its highest point (Point A) the string makes an angle of 55 degrees with the vertical. Its lowest point is Point B and Point C is where the string makes an angle of 35 degrees with respect to the vertical. Find the tension in the string and angular acceleration of the rock at (a) Point A, (b) Point B and (c) Point C.  (a) Draw a free body diagran of the kryptonite, including all relevant angles and axes at Point A, Point B, and Point C. (Three total FBD) (b) Find the angular speed, angular acceleration and tension in the string at Point A.  (c) Find the angular speed, angular acceleration, centripetal force and tension in the string at Point B. (d) Find the angular speed, angular acceleration, centripetal force and tension in the string at Point C.

A block of m = 2.00 kg hangs from a string that passes over a pulley with a moment of inertia / (to be determined) and a radius R = 0.44 m. The system of block and pulley is released from rest when the block is 5.00 m above the floor. It takes t = 1.17 s for the block to reach the floor. As the block accelerates downward, the pulley undergoes a counterclockwise angular acceleration. Using Newton's Laws (for linear and rotational motion), determine the moment of inertia I of the pulley. (Consider the linear acceleration of the block (from kinematics), the tension in the string, and the torque on the pulley. Careful with (+/-) directions} O 0.166 kg m² O 0.144 kg m² O 0.132 kg m2 O 0.173 kg m2 O 0.149 kg m2 30 F3 888 F4 esc F5 F6 #3 $ & 8

An object (with mass m = 6.20 kg) is attached to the free end of a massless string wrapped around a reel of radius R = 0.550 m and mass M = 4.00 kg. The reel is a solid disk, free to rotate in a vertical plane about the horizontal axis passing through its center, as shown in the figure. The suspended object is released from rest 3.50 m above the floor. Calculate the magnitude of the acceleration (in m/s2) of the object. Round your answer to 2 decimal places.Note: I=1/2 MR^2

= - = 6. A mass M₁ 10 kg resting on a horizontal frictionless surface is attached to a M₂ = 7 kg weight by a light wire that passes over a frictionless pulley. See figure. The pulley has the shape of a uniform disk of mass M3 4 kg and radius R 0.3 m. After the system is released, find (a) the tension in the wire on both sides of the pulley, (b) the acceleration of M₁, and (c) the horizontal and vertical forces that the axle exerts on the pulley. M1 M 3 M2