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?

A boy of mass m runs with speed v tangentially toward a merry-go-round of mass M and radius R, which is rotating with angular speed w. If the boy jumps on the merry-go-round, find the angular speed with which the system rotates once the boy is on top of the merry-go-round.

Modeled after the triatomic molecule problem that is let's consider the three atoms composing the molecule have different masses and coordinate, while the axis of rotation is still y-axis. The first atom has a mass of 7.281 kg, with x coordinate at 6.769 m and y coordinate at 9.989 m. The second atom has a mass of 61.310 kg, with x coordinate at 39.549 m and y coordinate at 25.180 m. The third atom has a mass of 49.316 kg, with x coordinate at 35.553 m and y coordinate at 31.216 m. What is the moment of inertia in the unit of kg m2 with respect to the y axis?

A ball weighing 800 grams and having a radius of 2cm moves in the direction of the positive x-axis at a speed of 5m/s. It collides with another stationary ball weighing 500 grams and also having a radius of 2cm. The collision occurs off-center, with the vertical components of the centers of the balls differing by 1cm. Following the collision, the lighter ball attains a speed of 3m/s. Determine the velocity of the heavier ball after the collision and calculate the amount of energy lost during the collision.

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?

In the figure, two satellites, A and B, both of mass m = 49.1 kg, move in the same circular orbit of radius r = 7410 km around Earth (mass ME = 5.98×1024 kg) but in opposite senses of rotation and therefore on a collision course. (a) Find the total mechanical energy EA+ EB of the two satellites + Earth system before the collision. (b) If the collision is completely inelastic so that the wreckage remains as one piece of tangled material (mass = 2m), find the total mechanical energy immediately after the collision. (c) Just after the collision, is the wreckage falling directly toward Earth’s center or orbiting around Earth?

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

A 500 kg piano is being lowered into position by a crane while two people steady it with ropes pulling to the sides. Bob’s rope pulls to the left, 15° below horizontal, with 500 N of tension. Ellen’s rope pulls toward the right, 25° below horizontal.a. What tension must Ellen maintain in her rope to keep the piano descending vertically at constant speed?b. What is the tension in the vertical main cable supporting the piano?

Four point masses are arranged in a square of side length L as shown. All of the masses are in the xy-plane.  Mass 2 and Mass 4 have mass of 4.6 kg, and Mass 1 and Mass 3 have a mass of 1 kg. If the side length L is 2.5 m, find the KE of the system if the point masses are rotated as a system around the y-axis (through m1 and m2) at 2.6 rad/sec.

In a rotational equilibrium experiment, a group takes a one-meter ruler with a uniformly distributed mass of 250 grams. A thread will be tied to the ruler 15 cm to the left of the center of mass, swinging the ruler. Then the group places a mass m1 = 170 gr at the 20 cm position on the ruler. Then they place a mass m2 = 155 gr in the 40 cm position. What must be the value of a mass m3 placed at the 15 cm position on the ruler for the system to remain in equilibrium?