4) A uniform disk and a hoop each have the same mass and radius. They each spin with the Which has the same angular velocity, around an axis that goes through their centers. largest kinetic energy and why?
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- 18) Consider an adult and a child riding their bikes. The adult's bicycle has tires with an outer diameter of 700 centimeters. The child's bicycle has tires with an outer diameter of 350 centimeters. The adult bicycle's tires are rotating with an angular velocity of 4.0 radians per second. If the child cyclist is traveling along the road at the same speed as the adult, then what angular velocity must the child's bicycle's tires be rotating at? [Assume the tires are rotating without slipping as the cyclists ride]. A) 1.0 radians second per B) 2.0 radians per second C) 4.0 radians per second D) 8.0 radians per second E) 16.0 radians per second abnoose e GProblem A) At a circus you see a man spinning plates with radii of 75 cm on top of long poles. The plates have a constant angular acceleration of 0.6 rad/s?. Assuming the plates start from rest, after a time of 8 seconds calculate a) how many revolutions they have made, b) their angular velocity, c) their tangential acceleration, d) their radial acceleration, and e) their overall acceleration, magnitude and direction with respect to the edge of the disk.3) Timmy (m, = 30.0 kg) is standing at the center of a merry-go-round that is spinning at 5.00 rad/s. The merry-go-round can be modeled as a disk with a diameter of 4.00 m and a mass of 50.0 kg, rotating on a frictionless axle though its center. He then walks to the edge of the merry-go-round. What is the new angular speed of the merry-go-round?
- Conservation of Angular Momentum Given data on two disks, such as masses and inner/outer diameters/radii, and the initial angular velocities of the 2 disks, use the conservation of angular momentum principle to calculate the common angular velocity after the two disks are allowed to contact each other and spin together. Or, given the common final angular velocity, solve for unknowns such as the initial angular velocity of one of the disks. Or, given data on the starting and final angular velocities and some data on the disks, solve for unknowns such as moments of inertia, masses or diameters/radii. EXAMPLE Two metal disks have masses m1=3.45 kg and m2=UNKNOWN kg, and each has a radius of 8.31 cm. (You may ignore the inner hole for both disks assume that it is very small.) They spin on cushions of air in a standard rotational dynamics apparatus. Initially, disk #1 is spinning counterclockwise at 6.02 rad/s and disk #2 is spinning clockwise at 2.50 rad/s. A pin is removed that drops disk…How can you show the relationship between applied torque and change in angular momentum?4. Two identical disks (same mass and radius) have a common axis. Initially one of the disks is spinning with a constant angular velocity. When the two disks are brought into contact, they stick together. Which of the following statements is true? (a) The total kinetic energy and the total angular momentum are unchanged from their initial values. (b) Both the total kinetic energy and the total angular momentum are reduced to half of their original values. (c) The total angular momentum is unchanged, but the total kinetic energy is reduced to half its original value. (d) The total angular momentum is reduced to one-half of its original value, but the total kinetic energy is unchanged. (e) The total angular momentum is unchanged, but the total kinetic energy is reduced to one-quarter of its original value.
- Number 12If you jump from a diving board and find that your body is rotating forward, you can spin your arms to stop the rotation and make your body land feet first. Explain in which direction you would rotate your arms and how this would help.4) A uniform 135-gram meter stick (length of 1 meter) rotates about an axis perpendicular to the stick passing through its center with an angular speed of 3.50 rad/s. What is the magnitude of the angular momentum of the stick?