6. A merry-go-round has a moment of inertia I = 740.0 kg.m² and radius of 2.30m. A child with m = 34.0kg runs at the merry-go-round (MGR) at v = 2.60m/s. His straight line path would miss the center of the MGR by a distance of 1.30m. What is his angular momentum relative to the MGR center before reaching it? If the MGR is initially at rest, what is its angular speed after the child jumps on assuming the child stays at the outer rim?
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- a top with radius 10cm, mass 2 kg has a string around the edge and is initially at rest. assume the top can be reasonably approximated as a solid cylinder. the top is held in place as the string is pulled. the string applies a force of 10N tangential to the edge for 2s. what is the angular velocity (in radians per second) of the top after 3 seconds? what is the angular momentum of the top after the string is pulled? after the string is pulled, the top is released. it travels away from its initial position at a linear velocity of 10m/s. what is the rotational velocity (in radians per s) at this top? assume no frictionAt the instant of the figure, a 7.20 kg particle P has a position vector of magnitude 1.10 m and angle e, = 40.0° and a velocity vectors lie in the xy plane. About the origin, what are the magnitude of (a) the angular momentum of the particle and (b) the torque acting on the particle? vector v of magnitude 1.80 m/s and angle 02 = 31.0°. Force F ,of magnitude 2.70 N and angle 03 = 31.0° acts on P. All three 0s 02 Units i (a) Number Units i (b) NumberA 10 kg particle moves in the xy plane with a velocity of v = (3.2 î-6.1 ) m/s. Determine the angular momentum of the particle when its position vector is 7 =(3 i +2.2 j) m. %3D O a:(-253.4k) kg.m2/s Ob:(+253.4 k) kg.m²/s OC(-25.34 k) kg.m²/s d(+25.34 k) kg.m²/s
- 4. A cylinder with mass m1 = 2.5 kg and radius r = 20 cm rotates counterclockwise about a vertical axis through its center with angular speed @1=5.0 rad/s. A second cylinder with mass m₂ = 1.0 kg and radius r1= 15 cm rotates clockwise about the same axis with angular speed @2 = 12 rad/s. The upper cylinder is lowered onto the lower one and they couple so they have the same rotational axis. Find the angular speed of the combination. Is kinetic energy conserved? If not, what happened to the a) b) kinetic energy? m₂ = 1.0 kg T2 = 15 cm m₁ = 2.5 kg n W₂ = 12 rad/s T₁ = 20 cm w₁ = 5 rad/s6.#1. Due to the conservation of angular momentum, moving mechanical parts in a spacecraft can affect the orientation and rate of angular rotation of the craft. Let us, crudely speaking, model Voyager II as a uniform disk with a mass of 720 kg and an effective radius of 1.0 meters. What is the moment of inertia of Voyager II under these assumptions? A.720kgm^2 B.580kgm^2 C.360kgm^2 D.180kgm^2 #1-1. Suppose the spacecraft in #1 is initially not rotating as a whole, and none of its compo- nents are rotating. A data tape spool with a moment of inertia of 1.25 × 10^−4 kg m^2 begins to spin at a rate of 15.5 Rad/s. What is the angular momentum of the spacecraft as a whole? A. 3.88×10^−3 kg·m^2/s B. 1.94×10^−3 kg·m^2/s C. 9.69×10^−4 kg·m^2/s D. 0.0 kg·m^2/s # 1-3. As the result of the tape spool operation, what is the magnitude of the angular speed of the spacecraft in #1-1 as a whole? A. 0.0 Rad/s B. 5.38 × 10^−6 Rad/s C. 1.07 × 10^−5 Rad/s D. 2.14 × 10^−5 Rad/s
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