What is the angular momentum of the disk after those rotations are complete, in kg m2/s?
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(Please answer to the fourth decimal place - i.e 14.3225)
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- A turntable with a mass of 12 kg and a radius of 2 meters spins at a constant angular velocity of 140 rpm. A 500-gram scoop of uniformly-dense ice cream falls onto the turntable, so the scoop's center of mass is one meter away from the turntable's center. The scoop forms a hemisphere and has a radius of 4 cm. If there's no friction between the brick and ice cream scoop and they spin at the same angular speed, what is their final angular speed, in rev/min or in rad/s? Justify your answer with your rationale and equations used. Moments of Inertia: Idisk =MR for rotation about its center of mass parallel to the z-axis. %3D Ihemisphere = MR for rotation about its center of mass parallel to the z-axis. Edit View Ansert Format Tools Table COREIa 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 frictionA solid cylinder of mass 4 kg and radius 2 m rotates with constant angular velocity of 5 rad/s about an axis through its center. What is the angular momentum of the cylinder?
- A disc (thin cylinder) of mass 0.05 kg and radius 0.65 m is rotating on a frictionless axle at a constant rate of 77 RPM. What a the angular velocity and angular momentum of the disc? の = rad/s L = kg-m2 A second disc of 0.02 kg and 0.23 m is dropped down the axle on top. The two then rotate together. What is the final angular velocity and RPM of the system of discs? rad/s RPM = RPMThe figure shows three uniform solid disks, each of mass 7.8 kg and radius 0.3 m rotating independently around a common axle. Two of the disks rotate in one direction at 5.3 rad/s while the other rotates in the opposite direction at 3.6 rad/s. Calculate the magnitude of the system's angular momentum about a point in the middle of the center disk. L= kg m²/s - Report your numerical answer below, assuming three significant figures. Remember to include a "-" when necessary.A disk is rotating about a vertical axis of rotation without displacing with an initial angular velocity of 10 rad/s. A 40 kg child is sitting 2 meters away from the axis of rotation. The rotational inertia of the disk is 50 kgm2 and the rotational inertia of the child is 80 kgm2. Another 40 kg child jumps onto the disk 3 meters away from the axis of rotation with a rotational inertia of 180 kgm2. Calculate the new angular velocity of the disk and two children.
- A disk is rotating about a vertical axis of rotation without displacing with an initial angular velocity of 10 rad/s. A 40 kg child is sitting 2 meters away from the axis of rotation. The rotational inertia of the disk is 50 kgm2 and the rotational inertia of the child is 80 kgm2. Another 40 kg child jumps onto the disk 3 meters away from the axis of rotation with a rotational inertia of 180 kgm2. Calculate the new angular velocity of the disk and two children.A cylinder has a cone removed from it. The cylinder and the conical hole have the same radius (2.06 meters) and height (4.56 meters). The cylinder has a density of 447 kg/m3. What is the rotational inertia of the cylinder with the cone removed in kg m2? You can set your origin at the tip of the cone, which is also the center of the base of the cylinder.The figure above shows Einstein spinning on a platform. He is initially spinning at a rate of 1rev/s, and holding his hands a distance of R1 = 80.3 cm away from his body. He then pulls his arms in to a distance of R2 = 40cm, changing his rotational speed. In this problem you can model Einstein’s body as a cylinder with a moment of inertia I = 30MR2, where M is his mass (60kg), and R is the distance his hands are from his body. (Notice that the figure shows him holding weights, but we are going to assume they are massless, to make it simpler!)(a) If he draws his arms in very quickly, you can safely ignore any frictional force on the platform. Assuming this is true, how fast is he rotating after he draws his arms in? (b) In reality, after he draws his arms in friction will start to slow him down. If this small amount of friction is applying a torque of 4 Nm to the platform, how long would it take before Einstein stops moving?
- A kid's merry-go-round in a park is a thin 150 kg disk (I = ½ MR2) with a radius of 3 m mounted to rotate freely about a central axis. On the edge of %3D the disk is an essentially massless bar. A 25 kg child jumps onto the bar (tangentially to the outer rim of the disk) at a speed of 12 m/s and a distance of 3 m from the rotation axis. If we think of the child as being essentially a point mass, what is the angular velocity of the system after the collision?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 = 15 rpm. Calculate the angular momentum of the wind turbine, in units of kilogram meters squared per second.A uniform disk of mass M is rotating freely about its center. On its rim lie a cockroach of mass M/9. Initially the cockroach and disk rotate together with an angular velocity of 3.2 rad/s. Then the cockroach walks halfway to the center of the disk. What is the new angular velocity of the system?