A 0.74-mm-diameter solid sphere can be rotated about an axis through its center by a torque of 10.8 m*Nm*N which accelerates it uniformly from rest through a total of 150 revolutions in 14.0 s.What is the mass of the sphere?
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- Three children are riding on the edge of a merry‑go‑round that has a mass of 105 kg and a radius of 1.40 m . The merry‑go‑round is spinning at 24.0 rpm. The children have masses of 22.0, 28.0, and 33.0 kg. If the 28.0 kg child moves to the center of the merry‑go‑round, what is the new angular velocity in revolutions per minute? Ignore friction, and assume that the merry‑go‑round can be treated as a solid disk and the children as point masses.The angular position of a point on a rotating wheel is given by 0 = 7.67+3.84t2 +3.65t3, where e is in radians and t is in seconds. At t= 0, what are (a) the point's angular position and (b) its angular velocity? (c) What is its angular velocity at t 8.10 s? (d) Calculate its angular acceleration at t = 2.83 s. (e) Is its angular acceleration constant? (a) Number Units (b) Number Units (c) Number i Units (d) Number i Units (e) NumberThe angular position of a point on a rotating wheel is given by 0 = 2.31 +2.92t² +2.52t³, where is in radians and t is in seconds. At t= O, what are (a) the point's angular position and (b) its angular velocity? (c) What is its angular velocity at t = 4.72 s? (d) Calculate its angular acceleration at t = 1.56 s. (e) Is its angular acceleration constant? (a) Number i Units (b) Number i Units (c) Number i Units (d) Number i Units (e) Number
- A playground merry-go-round has a mass of 100 kg and a radius of 1.80 m and it is rotating with an angular velocity of 0.500 rev/s. What is its angular velocity after a 22.0-kg child gets onto it by grabbing its outer edge? The child is initially at rest.A playground merry–go–round has a mass of 132 kg and a radius of 1.60 m and it is rotating with an angular velocity of 0.500 rev/s. What is its angular velocity after a 19.0–kg child gets onto it by grabbing its outer edge? The child is initially at rest.A figure skater performs a twisting jump. She rotates around her longitudinal axis 2 times in 0.65 s. What was her average angular velocity in radians/second? A 720rad/s B 19.3rad/s C 4? rad/s D 9.67 rad/s E 1107 rad/s
- Two girls (26 kg each) are standing on the edge of a solid, rotating disk of mass 70 kg and radius 1.3m. The initial angular speed of the disk is 0.71 rev/s. If one of the girls moves slowly toward the center while the other stays put at the edge, what is the new angular speed of the disk when she reaches the halfway point?A 22g ball moves from the centre to the outside edge of a 150g disk of radius 15.0 cm. The disk was initially rotating at 11.0 rad/s. What will be its final angular velocity? Treat the ballas a point mass. Inertia of the disk is(1/2)MRA 10 kg cylindrical barrel with a radius of 0.5 m rotates about a vertical axis of rotation without displacing with an initial angular velocity of 4 rad/s. The rotational inertia of the cylindrical barrel is 0.3mr2 and rain begins to fill the barrel with water as its rotating. If the barrel accumulates 4 kg of water, calculate the new angular velocity of the barrel.
- A wheel rotates clockwise about its central axis with an angular momentum of 600Kg.m 2 /s.At time t= 0, a torque of magnitude 50N.m is applied to the wheel to reverse the rotation. If the same torque is maintained, at what time will the angular momentum be counter-clockwise of 600Kg.m 2 /s?A dentist causes the bit of a high speed drill to accelerate from an angular speed of 1.76e4 rad/s to an angular speed of 3.71e4 rad/s. In the process, the bit turns through 1.62e4 rad.Assuming a constant angular acceleration, how long would it take the bit to reach its maximum speed of 8.42e4 rad/s starting from rest.A ball (in the form of a spherical shell which has a moment of inertia of 2/3 M R^2) rolls down a roof, then falls to the ground. The ball has a mass of 1.65 g and a radius of 15.0 cm. The roof is inclined at 20.0 degrees and the ball rolls a distance of 3 meters along the roof before falling off. a) What is the angular speed of the ball at the moment it leaves the roof? b) If the distance from the end of the roof to the ground is 2.50 m, how many revolutions does the ball make before it hits the ground?