The assembly can rotate around a perpendicular axis through point O at the left end. If we remove one particle (that is, 33% of the mass), by what percentage does the rotational inertia of the assembly around the rotation axis decrease when that removed particle is (a) the innermost one and (b) the outermost one? L. Axis (a) Number Units (b) Number Units
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- A neutron star of mass 2 x 10 kg and radius 11.1 km rotates with a period of 0.02 seconds. What is its rotational kinetic energy? KE = × 1012 J rot Question Help: Message instructor Submit QuestionA wheel with a radius of 12 cm rotates through 2.5 radians whileaccelerating from 1.2 rad/s to 6.2 rad/s.a) Calculate the angular acceleration.b) Determine the tangential acceleration.c) How long was the wheel accelerating?A typical small rescue helicopter has four blades: Each is 4.00 m long and has a mass of 50.0 kg. The blades can be approximated as thin rods that rotate about one end of an axis perpendicular to their length (I = (Ml^2)/3). The helicopter has a total loaded mass of 1000 kg. a.) Calculate the rotational kinetic energy in the blades when they rotate at 300 rpm. b.) Calculate the angular momentum of the four combined blades when they rotate at 300 rpm (Hint: Find the angular momentum for one blade and multiply it by 4).
- Two spheres of equal mass and radius arerolling across the floor with the same speed. Sphere 1 is a uniformsolid; sphere 2 is hollow. Is the work required to stop sphere 1greater than, less than, or equal to the work required to stop sphere2? (b) Choose the best explanation from among the following:I. Sphere 2 has the greater moment of inertia and hence thegreater rotational kinetic energy.II. The spheres have equal mass and speed; therefore, they havethe same kinetic energy.III. The hollow sphere has less kinetic energy.A disk at rest experiences a constant angular acceleration for t = 35 s, at the end of which it is spinning with a frequency of f = 35 rpm. Please answer the following questions. 1) Write an expression for the magnitude of the angular velocity of the disk after the acceleration in terms of the frequency. ω = 2) Calculate the magnitude of the angular velocity of the disk in rad/s at time t = 35 s. ω = 3) Write an expression for the average angular acceleration of the disk αave in terms of angular velocity. αave =a) Convert the following angles from degrees to radians: 15°, 35°, 80°, 95°, 180°b) Convert the following angles from radians to degrees: 0, π/6, 1.2π, 3, 6c) A propeller blade with a diameter of 5 m has an initial angular velocity of 42 rad/s and a constant angular acceleration of -15 rad/s2. What is the angular velocity after 5 revolutions? How much time does it take to complete these 5 revolutions?
- A 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 =MRA pitcher throws a curveball that reaches the catcher in 0.64 s. The ball curves because it is spinning at an average angular velocity of 260 rev/min (assumed constant) on its way to the catcher's mitt. What is the angular displacement of the baseball (in radians) as it travels from the pitcher to the catcher? Number Units2) A bicycle has wheels with radius of r=0.25m, and the bicycle is traveling at a constant speed of vb=4.00m/s. a) What is the angular speed of the wheels? b) What is the acceleration of a point on the outside edge of the bicycle tire? Draw a pictorial representation of the acceleration and velocity vectors at that point. c) The wheel slows down. Draw a pictorial representation of where the acceleration and velocity vectors now point. (for the same point on the outside edge of the bicycle tire).
- Consider a phonograph with a diameter of 0.6 m and a rotational speed of 33 RPM. Answer the following questions. What is its radius in m?What is its rotational speed in rad/s?What is the tangential speed on the phonograph's outer edge in m/s?What is the tangential speed at the center of the phonograph in m/s?What is the tangential speed halfway out to the edge of the phonograph?The wheel of an 80 cm diameter bicycle rotates at 50 rpm the moment a cyclist sees a pedestrian crossing. It applies the brake and comes to a complete stop 3 seconds later with constant deceleration during that period. Calculatea) The angular acceleration of the break.b) The number of turns made in 3 seconds.c) The angular velocity, period and frequency when the movement is UCM.d) Draw the velocity vector, the tangential acceleration vector and the normal acceleration vector for a point on the tire during braking.5. The plate shown moves in the xy plane. Knowing that (V₂), = 12 in./s, (V₂), = -4 in./s, and (Vc), = - 24 in./s, determine (a) the angular velocity of the plane, (b) the velocity of the point B, and (c) the point of the plate with zero velocity 4 in. 2 in. O [VA = (VA)xi + (VA)yj 2 in. VB = (UB)¸i + (UB)yj -6 in.- vc = (vc),i + (Vc)yj x