There is a uniform hollow spherical shell with a radius of 15 cm siting at the end of a massless rod with a length 5 cm and swings without friction about an axis. If it is released from rest above the axis, what is its angular velocity as it swings through directly below the axis?
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There is a uniform hollow spherical shell with a radius of 15 cm siting at the end of a massless rod with a length 5 cm and swings without friction about an axis. If it is released from rest above the axis, what is its
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- A uniform solid ball rolls without slipping down a plane which is inclined at 31° to the horizontal. If the ball has a radius r=0.4m, a mass m=0.1 kg and starts from rest, find: a) the speed of the ball after it travels 2m down the incline. b) at this point, what is the angular momentum of the ball? c) If the coefficient of friction between the ball and the plane is 0.25, what is the maximum angle of inclination that allows the ball to roll without slipping?A disk of mass M is spinning freely at 4.77 rad/s when a second identical disk, initially not spinning, is dropped onto it so that their axes coincide. In a short time the two disks are corotating. (a)What is the angular speed of the new system (in rad/s)? (b) If a third such disk is dropped on the first two, find the final angular speed of the system (in rad/s).Twin skaters approach one another and lock hands. (a) Calculate their final angular velocity, given each had an initial speed of 2.50 m/s relative to the ice. Each has a mass of 70.0 kg, and each has a center of mass located 0.800 m from their locked hands. You may approximate their moments of inertia to be that of point masses at this radius. (b) Compare the initial kinetic energy and final kinetic energy.
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- A space craft may be modeled as a uniform disk. Suppose the disk shaped craft has a mass of 2500 kg and a radius of 5.67 ngedalla par pplica meters. (a) What is the moment of inertia of the spacecraft? (b) Two rocket engines on opposite sides of the craft each apply an identical tangential force to impart a uniform angular acceleration in the counterclockwise sense. Suppose the craft acceleration from rest to an angular velocity of 1.00 revolutions per second in the counter clockwise sense over a period of 30.0 seconds. What is this final angular velocity in radians per second? (c) What is the angular acceleration of the craft over the period of uniform angular ac- celeration? (d) What net torque is needed to achieve the angular acceleration in part (c)? (e) What force is applied by each rocket engine during the period of uniform angular accel- eration?A bullet of mass 5.0 grams and velocity 330 m/s is shot into a wheel that is initially at rest. The wheel is solid disk ofmass 2.0 kg and radius 18 cm. The bullet strikes the edge tangentially and sticks to the edge. What are the disks finalangular velocity, angular momentum and rotational kinetic energy?A solid cylinder (disk) and a hollow cylinder are rolling with the same center- of-mass velocity v = 2 m/s on a level surface towards an incline. Both R cylinders have the same radius R and mass M. The moments of inertia are: 1 Solid cylinder 1, MR² Hollow cylinder I, = MR² (a) What is true about the kinetic energy when the cylinders are rolling on level ground? (i) they have the same translational kinetic energy (ii) they have the same rotational kinetic energy (iii) they have the same total kinetic energy [1] only (i) [2] only (ii) [3] (i) and (ii) [4] (i) and (iii) [5] (i), (ii), and (iii) (b) Which conservation law will allow you to calculate the final height? Conservation of: [1] momentum [5] moment of inertia [2] mechanical energy [3] kinetic energy [4] angular momentum (c) Calculate the maximum height the solid cylinder will reach before it rolls down again; please use g = 10 m/s². (d) Calculate the maximum height the hollow cylinder will reach before it rolls down again.
- A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is rotating at 10 rev/s; 60 revolutions later, its angular speed is 15 rev/s. Calculate (a) the angular acceleration, (b) the time required to complete the 60 revolutions, (c) the time required to reach the 10 rev/s angular speed, and (d) the number of revolutions from rest until the time the disk reaches the 10 rev/s angular speed.A 0.45 kg tetherball is attached to a pole and rotating in a horizontal circle of radius r₁ = 1.4 m and is circling at angular speed = 1.42 rad/s. As the rope wraps around the pole the radius of the circle shortens and became r2 = 0.9 m, that decreases the moment of inertia of the rotating tetherball. Neglecting air resistance what will be the angular speed of the ball after the rope is wrapped around the pole measured in kgm2/s (answer with 3 decimal places)? A