The 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 R, 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 Im = M•R², where R is the perpendicular distance from the point mass to the rotational axis. a) What is the final angular speed wf of the door (and dart stuck in it) after the dart finishes perforating it? b) At what final linear speed vy are the free edge of the door (close to the handle) and the dart moving together (relative to the ground) after the collision?

A spherical satellite of approximately uniform density with radius 4.8 m and mass 215 kg is originally moving with velocity (2600, 0, 0) m/s, and is originally rotating with an angular speed 2 rad/s, in the direction shown in the diagram. A small piece of space junk of mass 6.0 kg is initially moving toward the satellite with velocity (-2200, 0, 0) m/s. The space junk hits the edge of the satellite as shown in the figure below, and moves off with a new velocity ( 1300, 480, 0) m/s. Both before and after the collision, the rotation of the space junk is negligible. V3 L Part 1 Ux = Uy = @1 (a) Just after the collision, what are the components of the center-of-mass velocity of the satellite (v, and vy) and its rotational speed w? (For Ux, enter your answer to at least four significant figures.) Part 2 Mi @= i i Save for Later i M, R, 1 V2 m m/s m/s rad/s (b) Calculate the rise in the internal energy of the satellite and space junk combined. J Attempts: 0 of 10 used Submit Answer

Ballistic pendulum: A projectile of mass m = 1 kg is fired with an initial speed v0 = 20 m/s at the bob of a pendulum with radius R = 3 m. The bob has mass M = 4 kg and is suspended by a rod of negligible mass. After the collision the projectile and bob stick together and swing at speed vf through an arc reaching height h and stop. (assume g=10 m/s2) (1) What is the speed vf just after the collision ?  (2) What is the total kinetic energy for projectile and bob together just after the collision?

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A 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?

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) Number

Two spheres of masses m = 1.07 g and m' = 1.10 * 10 ^ 2 kg are isolated from all other bodies and are initially at rest, with their centers a distance r = 14 cm apart. One min later , the smaller sphere has moved 0.585 mm toward the larger sphere, Compute the acceleration and the value of g. Acceleration=? Value g =

Two 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

The position vector of a particle of mass 1.0 kg as a function of time is given by F= (6f + 10 tj ) m where 7 is in meters and t is in seconds. Determine the angular momentum of the particle about the origin as a function of time (in kg m2/s)? Option 1 Option 2 Option 3 Option 4 Option 5 (20 tj) (120 tj) (60 tj) (30 tj) (240 tj)

A physical pendulum consists of a vertical board of of mass 5.8 kg, length 172 cm, and width 5 cm hanging from a horizontal, frictionless axle. A bullet of mass 145 g and a purely horizontal speed v impacts the pendulum at the bottom edge of the board. The board then makes a complete circle. (a) If the bullet embedded itself in the board, what is the minimum speed the bullet could have to make this so? (b) If the bullet passed through the board, reducing its speed by 1/5 its original value, what is the minimum speed of the bullet? (c) If the bullet is made of rubber and rebounds elastically, what is the minimum speed the bullet could have? (d) What is the rebound speed of the bullet?