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- q4A rotating solid sphere, (mass = 1kg, radius = 25 cm) starts to spin from rest with a constant angular acceleration of a =1.5 rad / s². After 5s, what is: • The angular velocity of the sphere • The number of rotations (please include fractional answers) The rotational kinetic energy of the sphere if I =MRTwo wheels are connected by a belt that does not slip. The smaller wheel has a diameter D, while the bigger wheel has a diameter that is 4.00 times bigger. Calculate the ratio of the moments of inertia if the two wheels have: i) the same angular momentum about their rotation axes. ii) the same rotational kinetic energy.
- The moment of inertia of an object about a certain axis is 1.2 kg-m2. Initially the object is at rest, and then it is accelerated at a constant rate of 25 rad-s-2. Determine the time required for the object to achieve a rotational kinetic energy of 1.50 kJ.A 366-N force is applied at A as shown. y = 370 mm. Determine (b) the smallest force applied at B that creates the same moment about D. Write numerical value and 2 decimal places. + for counterclockwise -100 mm- -200 mm y mm 25° A P D 125 mm C BTwo astronauts, each having a mass M, are connected by a rope of length d having negligible mass. They are isolated in space, moving in circles around the point halfway between them at speed v. c) By pulling on the rope, the astronauts shorten the distance between them to d/2. What is the new angular momentum of the system?d) What are their new speeds?e) What is the new rotational energy of the system?f) How much work is done by the astronauts in shortening the rope?