A 550.0 g bird is flying horizontally at 2.50 m/s, not paying much attention, when it suddenly flies into a stationary vertical bar, hitting it 25.0 cm below the top. The bar is uniform, 0.700 m long, has a mass of 1.50 kg kg, and is hinged at its base. The collision stuns the bird so that it just drops to the ground afterward (but soon
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- A diver (m = 60 kg) jumps from a diving board. At takeoff, his angular momentum about the transverse axis is 30 kg⋅m2/s. His radius of gyration about the transverse axis is 0.5 m at this instant. During the dive, he tucks and reduces his radius of gyrations about the transverse axis to 0.2 m. At takeoff, what is the diver’s moment of inertia about his transverse axis?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 BulletThe moment of inertia I of a cheap door of mass M = 4.00 kg (about an axis going through the hinges at the door frame) is I= (1/3) M · R², where R= 0.960 m is the width of the door. The door is initially open and at rest. The door suddenly is struck by a huge and heavy dart of mass m = 0.300 kg traveling perpendicular to the plane of the door at a speed vi = 20.0 m/s. The dart perforates the wooden door getting permanently stuck at the point of impact, which happened to be right next to the free vertical edge of the door (close to the handle). Because the dimensions of the dart are so small (even though they are exaggerated in the picture for clarity) compared to its distance R to the rotational axis (the distance from the hinge to the free vertical edge next to which the dart strikes the door, which is the width of the door R) we can treat the dart as a point mass. I remind you that we learned in class that the moment of inertia of a point mass is I, = m-R², where R is the…
- A weather vane initially at rest has a moment of inertia of 0.104 kg · m2 about its axis of rotation. A 68.0 g piece of clay is thrown at the vane and sticks to it at a point 14.0 cm from the axis. The initial velocity of the clay is 27.5 m/s, directed perpendicular to the vane. Find the angular velocity of the weather vane just after it is struck.A uniform thin rod of length 0.17 m and mass 4.5 kg can rotate in a horizontal plane about a vertical axis through its center. The rod is at rest when a 4.4 g bullet traveling in the rotation plane is fired into one end of the rod. As viewed from above, the bullet's path makes angle 0 = 60° with the rod. If the bullet lodges in the rod and the angular velocity of the rod is 10.0 rad/s immediately after the collision, what is the bullet's speed just before impact? Number Units Axis eA rod of mass M = 3.25 kg and length L can rotate about a hinge at its left end and is initially at rest. A putty ball of mass m = 65 g, moving with speed v = 5.25 m/s, strikes the rod at angle θ = 51° from the normal at a distance D = 2/3 L, where L = 1.3 m, from the point of rotation and sticks to the rod after the collision. 1. What is the angular speed ωf of the system immediately after the collision, in radians per second?
- In the figure, a 7.90 g bullet is fired into a 0.430 kg block attached to the end of a 0.140 m nonuniform rod of mass 0.578 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 0.0761 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 3.64 rad/s, what is the bullet's speed just before impact?Two 3.40 kg balls are attached to the ends of a thin rod of length 44.0 cm and negligible mass. The rod is free to rotate in a vertical plane without friction about a horizontal axis through its center. With the rod initially horizontal (the figure), a 73.0 g wad of wet putty drops onto one of the balls, hitting it with a speed of 2.97 m/s and then sticking to it. (a) What is the angular speed of the system just after the putty wad hits? (b) What is the ratio of the kinetic energy of the system after the collision to that of the putty wad just before? (c) Through what angle (deg) will the system rotate before it momentarily stops? Putty wad Rotation axis (a) Number i Units (b) Number i Units Units i (c) NumberTwo 3.50 kg balls are attached to the ends of a thin rod of length 36.0 cm and negligible mass. The rod is free to rotate in a vertical plane without friction about a horizontal axis through its center. With the rod initially horizontal (the figure), a 42.0 g wad of wet putty drops onto one of the balls, hitting it with a speed of 3.25 m/s and then sticking to it. (a) What is the angular speed of the system just after the putty wad hits? (b) What is the ratio of the kinetic energy of the system after the collision to that of the putty wad just before? (c) Through what angle (deg) will the system rotate before it momentarily stops? Putty wad Rotation axis
- Ant-Man is walking around on top of a wooden plank that rests atop two thin, vertical steel pillars, which are bolted into the ground. Ant-Man's mass is m₁ = 80.0 kg, but he is small enough to be treated as a point particle. The plank (m₂ = 11.7 kg) has a length of L = 2.44 m, with the left end flush against the edge of the left pillar. The separation distance between the pillars is d 1.50 m. T Suppose that Ant-Man walks far enough out from the right pillar so that the plank is just about to start rotating. What will be the magnitude of the force from each of the pillars on the plank at this time? (Hint: begin your analysis by thinking about the torques acting on the plank, and note that the forces from the two pillars are not the same.) How far out from the right pillar could Ant-Man walk before the plank starts to rotate?A solid disk rotates in the horizontal plane at an angular velocity of 0.0652 rad/s with respect to an axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.113 kg·m2. From above, sand is dropped straight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance of 0.393 m from the axis. The sand in the ring has a mass of 0.487 kg. After all the sand is in place, what is the angular velocity of the disk?A solid disk rotates in the horizontal plane at an angular velocity of 4.20 × 10-2 rad/s with respect to an axisperpendicular to the disk at its center. The moment of inertia of the disk is 0.14 kg.m2. From above, sand is droppedstraight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance of 0.40 m from the axis.The sand in the ring has a mass of 0.50 kg. After all the sand is in place, what is the angular velocity of the disk?