A barbell spins around a pivot at its center at A. The barbell consists of two small balls, each with mass 500 grams (0.5 kg), at the ends of a very low mass rod of length d = 30 cm (0.3 m; the radius of rotation is 0.15 m). The barbell spins clockwise with angular speed 100 radians/s. m m II: Treat the object as one barbell (h) Calculate the moment of inertia I of the barbell. I = kg Â. m2 (j) Use the moment of inertia I and the angular speed || = 100 rad/s to calculate the rotational angular momentum of the barbell: ka Ô, m2/s

A light rigid rod 1.00 m in length rotates about an axis perpendicular to its length and through its center as shown below. Two particles of masses 4.00 kg and 3.00 kg are connected to the ends of the rod. What is the angular momentum of the system if the speed of each particle is 6.60 m/s? J.s 3.00 kg 1.00 m 4.00 kg

Three children are riding on the edge of a merry-go-round that is 102 kg, has a 1.60 m radius, and is spinning at 17.3 rpm. The children have masses of 22.4, 30.5, and 40.8 kg. If the child who has a mass of 40.8 kg moves to the center of the merry-go-round, what is the new angular velocity in rpm? rpm

An audio compact disk (CD) player is rotating at an angular velocity of 32.5 radians per second when playing a track at a radius of 4.0 cm. What is the linear speed at that radius? What is the rotation rate in revolutions per minute?

Q3. Consider two disks in essentially the same plane, and rotating about the common center O with different but constant angular velocities. Let the angular velocities by w and w'. The radii of the disks are r and r'. Two points P and P' are located at the outer edges of the disks. Assume that point O is fixed. Find the velocity and acceleration of P' relative to P at the time instant when the two points have the least separation, in the following two cases: (a) the observer is fixed to the ground, or nonrotating; (b) the observer is rotating with the unprimed system, i.e., the disk with radius r and angular velocity w. Express the results in terms of the unit vectors e; and en which rotate with the unprimed system. (Problem 2-15 in the text).

3. The figure to the right shows a rod that is connected to a frictionless table through a pin-labeled by A -placed through the center of it. (You are looking down on the table.) The rod has mass m and length l. Although the rod is initially at rest, it can rotate freely (without friction) about the pin. A small particle with mass m/3, and moving with an initial velocity vo vo collides with the end of the rod. After the collision the mass stops moving, and the rod starts rotating with angular velocity w. I would strongly recommend that you draw a free body diagram for the rod in parts a and b. a. Linear momentum is not conserved for this collision. Explain in detail why. b. Angular momentum is conserved about the pivot. Explain in detail why. c. What is w? Express it in terms of vo, and l. d. Is energy conserved in the collision? Justify your answer by calculating the change in energy of the system in the collision. e. After a time T after the collision the rod will rotate around and…

A light rigid rod of mass 3.00 kg and length 2.00 m rotates about an axis perpendicular to its length and passing through its center as shown in the figure below. Two particles of masses m1 = 6.00 kg and m2 = 3.50 kg are connected to the ends of the rod. What is the angular momentum of the system if the speed of each particle is 4.05 m/s? m2

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A solid, uniform, spherical boulder (I=(2/5) MR2) starts from rest and rolls down a 75.0 [m] hill, as shown at the figure at the right. The top half of the hill is rough enough to cause the boulder to roll without slipping, but thelower half is covered with ice and there is no friction. What is the translational speed of the boulder when it reaches the bottom of the hill?

You are swinging a sling shot, which is basically a string tied to a rock, vertically as shown. After you get it going fairly fast, you hold your hand stationary so it swings around in a perfect circle. The rock slows down as it gets higher and speeds up as it comes back down. One simple model for how this would work is that the tangential component of the rock's velocity isvt(t)=v0-(v0/4)sin((2pi/T)t)  where v0 is the rock's speed at t=0s and T is the time it takes the rock to go all the way around the circle. Call L the length of the string. 1. What is the total acceleration of the rock? 2. What is the angular Acceleration?