Shown below is a small particle of mass 27 g that is moving at a speed of 10 m/s when it collides with and sticks to the edge of a uniform solid cylinder. The cylinder is free to rotate about the axis through its center and perpendicular to the page. The cylinder has a mass of 0.7 kg and a radius of 14 cm and is initially at rest 10 m/s Before After (a) What is the angular velocity (in rad/s) of the system after the collision? (Indicate the direction with the sign of your answer.) rad/s (b) How much kinetic energy (in 3) is lost in the collision? J
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- The uniform thin rod in the figure below has mass M = 2.00 kg and length L = 3.25 m and is free to rotate on a frictionless pin. At the instant the rod is released from rest in the horizontal position, find the magnitude of the rod's angular acceleration, the tangential acceleration of the rod's center of mass, and the tangential acceleration of the rod's free end.A uniform solid ball rolls without slipping down a plane which is inclined at 31° to the horizontal. If the ball has a radius r=0.4m, a mass m=0.1 kg and starts from rest, find: a) the speed of the ball after it travels 2m down the incline. b) at this point, what is the angular momentum of the ball? c) If the coefficient of friction between the ball and the plane is 0.25, what is the maximum angle of inclination that allows the ball to roll without slipping?The figure shows three 0.0146 kg particles that have been glued to a rod of length L-5.58 cm and negligible mass. 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? (a) Number (b) Number Axis Units Units 0 m m m |a+d+d+
- A baseball has a mass of 0.15 kg and radius 3.7 cm. In a baseball game, a pitcher throws the ball with a substantial spin so that it moves with an angular speed of 41 rad/s and a linear speed of 34 m/s. Assuming the baseball to be a uniform solid sphere, determine the rotational and translational kinetic energies of the ball in joules. KErotational = KE translational =A playground merry-go-round (a solid disk) has a mass of 120 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 (who is initially at rest) gets onto it by grabbing its outer edge? (You can approximate the child as a point mass). (Hint: here you'll need to use the conservation of angular momentum.) a. 0.683 rev/s b. 0.415 rev/s c. 0.366 rev/s d. 0.129 rev/sA 20-kg child running at 1.4 m/s jumps onto a playground merry-go-round that has mass 180 kg and radius 1.6m. She is moving tangent to the platform when she jumps and she lands right on the edge. What is the angular velocity of the child and the merry-go-round if the merry-go-round started from rest? You can treat the merry-go-round as a solid disc and ignore any friction in its axle. Please answer in units of rad/sec.
- A student holds a bike wheel and starts it spinning with an initial angular speed of 9.0rotations per second. The wheel is subject to some friction, so it gradually slows down. In the 10 s period following the inital spin, the bike wheel undergoes 70 complete rotations. Assuming the frictional torque remains constant, how much more time Δts will it take the bike wheel to come to a complete stop? The bike wheel has a mass of 0.625 kg and a radius of 0.315 m. If all the mass of the wheel is assumed to be located on the rim, find the magnitude of the frictional torque τf that was acting on the spinning wheel.Shown below is a small particle of mass 27 g that is moving at a speed of 10 m/s when it collides with and sticks to the edge of uniform solid cylinder. The cylinder is free to rotate about the axis through its center and perpendicular to the page. The cylinder has a mass of 0.3 kg and a radius of 14 cm and is initially at rest. 10 m/s Before After (a) What is the angular velocity (in rad/s) of the system after the collision? (Indicate the direction with the sign of your answer.) X rad/s (b) How much kinetic energy (in J) is lost in the collision? JThe figure shows a small particle of mass 0.278 kg that is moving with a speed of 7.29 m/s when it collides and sticks the the edge of a uniform solid cylinder. The cylinder is free to rotate about an axis through its center. The cylinder has a mass of 2.677 kg, and a radius of 0.28 m, and is initially at rest. What is the angular velocity of the system after the collision? Express your answer in radians/s to 3 significant figures. Before After