A solid disk has a radius of 0.084 m and a mass of 5.33 kg. What is the rotational kinetic energy of the disk when it rotates at a rate of 651 rpm, in units of joules?
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- A solid cylinder with a mass of 300.0g and a radius of 20.0cm is rotating at 50.0 rad/s. A metal hoop of mass 200.0g and radius 10.0cm, initially not rotating, is dropped onto the rotating solid cylinder so that their rotational axes align. Determine the angular speed of the 2 objects as they rotate together. Report your answer in radians per second, but only enter in the numerical value.The angular position of a rotating object is given by the equation 0 = a + bt + ct2 where a, b, and c are constants. Here a = 1.44 rad, b = 2.00 rad/s, and c = 3.06 rad/s2. (a) What is the position of the object at t1 = 0 and t2 = 4.00 s? 01 rad 02 rad (b) What is the angular speed of the object at t1 = 0 and t, = 4.00 s? %3D rad/s @2 = rad/s (c) What is the angular acceleration of the object at t, = 0 and t, = 4.00 s? a1 = rad/s? rad/s?A neutron star of mass 2.0 x 103° kg and radius 10 km rotates with a period of 0.02 seconds. What is its rotational kinetic energy (in J)?
- A 24 g block sits at the center of a turntable that rotates at 80 rpm. A compressed spring shoots the block radially outward from the center along a frictionless groove in the surface of the turntable. Calculate the turntable's angular speed when the block reaches the outer edge. Treat the turntable as a solid disk with mass with mass 200 g and diameter 54.0 cm. Express your answer in revolutions per minute.A playground merry-go-round has a radius of 3.5 m and a rotational inertia of 720 kgˑm2. It is initially spinning at 0.60 rad/s when a 25 kg child crawls from the center to the rim. When the child reaches the rim the angular velocity of the merry-go-round in rad/s is:The answer is supposed to be v=2.56m/s but I'm not sure how to write out the problem.
- The rotational inertia of a disk about its axis is 8.3kg. m². When a 3.2 kg weight is added to its rim, 9.7 m from the axis, the rotational inertia becomes: Answer:The rotational inertia of a disk about its axis is 0.40 kg ˑm 2. When a 5.0-kg weight is added to its rim, 0.60 m from the axis, the rotational inertia in kg ˑm 2 becomes:A spherical shell with 0.13 kg of mass and 0.050 m of radius rolled without slipping on a horizontal floor. A ramp was placed on the floor. The spherical shell rolled up the incline without slipping to a vertical height of 0.46 m before stopping. The ramp has a length of 1.8 m along the incline. Find the speed of the spherical shell before it reached the ramp. Hint: the spherical shell has rotational kinetic energy. The rotational inertia of a spherical shell is (2/3)mr^2.
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