la) A “dumbbell" used in the energy conservation in rotational motion lab, consists of a cylindrical rigid rod with two 0.2 kg masses fixed at the ends. The mass of the rod is negligible when compared to the two masses. The diameter of the rod is 8 mm and its length is 20 cm. The rod is rotating about its center (with the axis of rotation perpendicular to the length of the rod as in today's experiment). What is the moment of inertia of this system?

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We will assume that the velocity of Juan's hand and the pencil were both 0.9 meters per second prior to impact and that his wrist added an angular velocity to the pencil of 7.4 radians/second. In reality the pencil dug in nearest to my thumb and did not poke through the back. For the purpose of this calculation we will instead say that the blue pencil of mass M and length of L pushed through my hand until 20% of its length was behind the hand. We will further assume that the normal force between the hand and the pencil was 120 Newtons and that the area of the point of the pencil was 0.0024mm2. The coefficient of kinetic friction between the pencil exterior and my flesh was 0.24 because I was running a slight fever and had a temperature of 102 degrees Fahrenheit.  Write an expression for dm: dm =     Write the result for the Moment of Inertia: I = The formula for Moment of Inertia in the form of an integral: I = ∫ Write an expression for the upper limit of the integral: Upper Limit…

The figure shows a small piece of clay colliding into a disk. The disk is initially at rest, but can rotate about a pivot fixed at its center. The collision is completely inelastic.1) The disk has mass M = 4.73 kilograms and radius R = 0.755 meters. The clay has mass m = 279 grams and is moving horizontally at vi = 3.66 m/s just before colliding with and sticking to the disk. The clay strikes the edge of the disk at a location of b = 0.505 meters offset from the center of the disk. Note that the size of the clay is negligible compared to the radius of the disk. 2) Calculate the angular velocity (rad/s) of the disk just after the collision.

A 10 kg wheel with a 0.4 meter radius is rotating at 4 rad/s. A 8 Nm torque is applied to the wheel. The rotational inertia of the wheel is 0.48 kgm2. The angular momentum of the wheel changes by 4 kg*m2/s. How long was the torque applied to the wheel.

A sanding disk with rotational inertia 0.0012 kg-m2 is attached to an electric drill whose  motor delivers a torque of magnitude 15 N-m about the central axis of the disk.  About that axis and with a torque applied for 48 millisecond, what is the magnitude of the angular momentum?

A uniform thin rod of length 0.70 m and mass 5.5 kg can rotate in a horizontal plane about a vertical axis through its center. The rod is a rest when a 3.0-g bullet traveling in the horizontal plane of the rod is fired into one end of the rod. As viewed from above, the direction of the bullet velocity makes an angle of 60° with the rod (see the figure). If the bullet lodges in the rod and the angular velocity of the rod is 11.0 rad/s immediately after the collision, what is the magnitude of the bullet's velocity just before impact?

4. 4. A dancer on ice spins faster when she folds her arms. This is due to A an increase in kinetic energy and an increase in angular momentum 8 a decrease in kinetic energy and an decrease in angular momentum C constant kinetic energy and a decrease in angular momentum o an increase in kinetic energy and constant angular momentum E and increase in kinetic energy and a decrease in angular momentum

Kristen is spinning on the ice at 20 rad/s about her longitudinal axis when she abducts her ärms and doubles her radius of gyration about her longitudinal axis from 30 cm to 60 cm. If her angular momentum is conserved, what is her angular velocity about her longitudinal axis before abduction? After abduction?