A student sits at rest on a piano stool that can rotate without friction. The moment of inertia of the student-stool system is 4.5 kg. m². A second student tosses a 2.0 kg mass with a speed of 3.0 m/s to the student on the stoole, who catches it at a distance of 0.40 m from the axis of rotation. Assume a right angle between the ball trajectory and radius drawn to the catch point.
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- A merry-go-round is a common piece of playground equipment. A 3.0-mm-diameter merry-go-round, which can be modeled as a disk with a mass of 260 kgkg , is spinning at 17 rpmrpm. John runs tangent to the merry-go-round at 5.4 m/sm/s, in the same direction that it is turning, and jumps onto the outer edge. John's mass is 30 kgkg. Part A What is the merry-go-round's angular velocity, in rpmrpm, after John jumps on? Express your answer in revolutions per minute.In the figure, a 7.42 g bullet is fired into a 0.531 kg block attached to the end of a 0.914 m nonuniform rod of mass 0.909 kg. The block- rod-bullet system then rotates in the plane of the figure, about a fixed axis at A. The rotational inertia of the rod alone about A is 0.0305 kg-m2. Treat the block as a particle. (a) What then is the rotational inertia of the block-rod-bullet system about point A? (b) If the angular speed of the system about A just after impact is 3.51 rad/s, what is the bullet's speed just before impact? A Rod Block Bullet (a) Number i Units (b) Number i UnitsThree children are riding on the edge of a merry-go-round that is 182 kg, has a 1.60 m radius, and is spinning at 15.3 rpm. The children have masses of 19.9, 28.5, and 32.8 kg. If the child who has a mass of 28.5 kg moves to the center of the merry-go-round, what is the new angular velocity in rpm?
- Basketballs are basically hollow spheres with moment of inertia 2/3 MR?. One basketball has diameter of 9.5 inches (24.1 cm) and a mass of 623 grams. If the basketball starts from rest and rolls down a hill 10.0 m high without skidding, what will the basketball's linea speed be at the bottom of the hill? Ignore air friction. Please answer in units of m/sec.Paralel axis theorem) = 0.108m Isaいd ニ Sphere MR? しR-0.1og。 A bowling ball of mass 7.1 kg and diameter 21.6 am is thrown down the alley at a speed of 8.7 m/s. The bowling ball is initially skidding, with no angular velocity, down the alley. The coefficient of friction between the ball and the alley is (0.30, 0.25). Motion Information Event 1:1 Free-Body Diagram Event 2: re byl! t, =0 12 = いitroa* Sipi. 12 = 02 = 0, = V; = 8,7mls 01 = 0 V2 = 02 = aj = KF az = a2 = aj = Mathematical Analysis V½ =WqRt Cond,i tionof event 2 untilthen, The FBD aboveis vali?, and ball AiCcedernting 2 EF=- "F = Mamg = ma> a= -Meg * MR G: EF:0 :f - mg F:mg a £ Roc 5 MM g %3D %3D => 2 R Calculate %3D Vz = V, + a€z the rest is easy Solve for te...A wheel on a car has an angular momentum of 5.00 kg m2/s. If the radius of the wheel is 0.25m, what is the wheel’s angular velocity?A "Lazy Susan" food tray is being rotated by a person in quest of sustenance. Suppose the person exerts a 2.60 N force perpendicular to the Lazy Susan's 0.260 m radius for 0.240 s. (a) What is the final angular momentum of the Lazy Susan, in kg · m²/s, if it starts from rest, assuming friction is negligible? 0.16224 kg. m²/s (b) What is the final angular velocity of the Lazy Susan in rev/s, given that its mass is 2.80 kg and assuming its moment of inertia is that of a disk? X The Lazy Susan is in the form of a solid disk. rev/sA disk-shaped merry-go-round of radius 2.53 mm and mass 135 kg rotates freely with an angular speed of 0.641 rev/s . A 65.4 kg person running tangential to the rim of the merry-go-round at 3.51 m/sm/s jumps onto its rim and holds on. Before jumping on the merry-go-round, the person was moving in the same direction as the merry-go-round's rim. What is the final angular speed of the merry-go-round?Angular momentum is conserved for this inelastic collision because the surface is frictionless and the unbalanced external force at the nail exerts no torque. The disk has a mass of 51.5 g and an initial velocity of 32.0 m/s when it strikes the stick that is 1.40 m long and 2.05 kg at a distance of 0.100 m from the nail. 1. What is the angular velocity (in rad/s) of the two after the collision? (magnitude in rad/s) 2. What is the kinetic energy (in J) before and after the collision? Kbefore= J Kafter= J 3. What is the total linear momentum (in kg · m/s) before and after the collision? (Entermagnitude) pbefore= kg · m/s pafter= kg · m/sA 5.0-m radius playgorund merry-go-round with a moment of inertia of 2000 Kg*m2is rotating freely with an angular speed of 2.0 rad/s. Two people, each having a mass of 60 Kg, are standing right outside the edge of the merry-go-round and step on it with negligible speed. what is the angular speed of the mery go round right after the two people have stepped on?A 3.0 kg particle moves in a circle of radius 2.0 m with an angular momentum of 30.0 kg⋅m2/s. What is its speed of rotation?In the figure, a 6.04 g bullet is fired into a 0.604 kg block attached to the end of a 0.904 m nonuniform rod of mass 0.435 kg. The block- rod-bullet system then rotates in the plane of the figure, about a fixed axis at A. The rotational inertia of the rod alone about A is 0.0372 kg-m2. Treat the block as a particle. (a) What then is the rotational inertia of the block-rod-bullet system about point A? (b) If the angular speed of the system about A just after impact is 5.03 rad/s, what is the bullet's speed just before impact? Rod Block BulletSEE MORE QUESTIONS