A ball (solid sphere) with a mass of 0.5 kg and radius 30 cm is rolling on a horizontal surface at speed v = 3.5 m/s when it reaches a 25° incline. How far along the incline will it go? (Moment of inertia of a solid sphere is I= 2/5 MR)
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- A deep-sea fisherman hooks a big fish that swims away from the boat, pulling the fishing line from his fishing reel. The whole system is initially at rest, and the fishing line unwinds from the reel at a radius of 4.50 cm from its axis of rotation. The reel is given an angular acceleration of 110 rad/s2 for 2.00 s. Find the number of revolutions per minute the reel makes. the final answer must be 3 decimal places.A turntable (disk) of radius r= 25.0 cm and rotational inertia 0.395 kg · m rotates with an angular speed of 3.04 rad/s around a frictionless, vertical axle. A wad of clay of mass m = 0.254 kg drops onto and sticks to the edge of the turntable. What is the new angular speed of the turntable? rad/sDuring a tennis serve, a racket is given an angular acceleration of magnitude 170 rad/s2. At the top of the serve, the racket has an angular speed of 13.0 rad/s. If the distance between the top of the racket and the shoulder is 1.50 m, find the magnitude of the total acceleration of the top of the racket.
- A flywheel with a diameter of 1.81 m is rotating at an angular speed of 197 rev/min. (a) What constant angular acceleration (in revolutions per minute-squared) will increase the wheel's angular speed to 929 rev/min in 63.9 s? (b) How many revolutions does the wheel make during that 63.9 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 cylinder with a diameter of 23 cm rolls with an angular speed of 0.30 rad/s on a level surface. If the cylinder experiences a uniform tangential acceleration of 0.022 m/s2 without slipping until its angular speed is 1.01 rad/s, (a) Through how many complete revolutions does the cylinder rotate during the time it accelerates?
- A Texas cockroach walks from the center of a circular disk (that rotates like a merry-go-round without external torques) out to the edge at radius R. The angular speed of the cockroach–disk system for the walk is (va = 5.0 rad/s and vb = 6.0 rad/s). After reaching R, what fraction of the rotational inertia of the disk does the cockroach have?A thin rod has a length of 0.537 m and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of 0.778 rad/s and a moment of inertia of 1.10 x 10³ kg-m². A bug standing on the axis decides to crawl out to the other end of the rod. When the bug (whose mass is 5 x 10-3 kg) gets where it's going, what is the change in the angular velocity of the rod?A cylinder 32.6 cm in diameter is at rest initially. It is then given an angular acceleration of 14.5 rad/s^2. Find the tangential speed of the outer edge of the cylinder at 6.08 s. Give your answer in m/s.
- While placing a compact disc into a CD player, you notice a small chip on its edge. You attempt to play the CD anyway by placing the CD into the player's deck with the chip at 0o = 12.6° as measured from the +x-axis. The CD begins to rotate with angular acceleration a = 2.31 rad/s². If the CD has been spinning for t = 3.51 s and the disc has a radius of r = 6.00 cm, what are the x-y coordinates of the chip after this time, assuming the center of the disc is located at (0.00,0.00). X = y = cm cmA disk, initially rotating at 114 rad/s, is slowed down with a constant angular acceleration of magnitude 2.39 rad/s2. (a) How much time does the disk take to stop? (b) Through what angle (rad) does the disk rotate during that time?A thin rod has a length of 0.792 m and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of 0.939 rad/s and a moment of inertia of 1.41 x 103 kg-m². A bug standing on the axis decides to crawl out to the other end of the rod. When the bug (whose mass is 5 x 10-³ kg) gets where it's going, what is the change in the angular velocity of the rod?