Earth spins around its own axis and orbits Sun. Calculate Earth's total kinetic energy and Earth's total angular momentum about Sun. Assume that Sun is so massive compared to Earth that the center of mass of the system is at Sun's center.
A pendulum is composed of a 0.1-kg steel ball that is attached to the end of a 0.75 m long lightweight string. You pull the ball to the right to an angle of 30 and release it from rest.
A rod can rotate about an axis perpendicular to the page and through the left end of the rod as shown. The forces shown in the image are applied to the rod. is applied at the end of the rod, is applied to the middle of the rod, and is applied at one-fourth the length of the rod. The length of the rod is 0.5 m. All forces have a magnitude of 75 N.
What is the net torque on the rod?
A 20 kg child runs at a constant speed of 3.0 m/s, in a straight line tangentially to a merry-go-round, and jumps onto the edge of the merry-go-round of radius 2.0 m, as shown below.
Here's a new invention for a "catching-machine'' that catches a baseball and tells you the speed of the ball based on how fast the machine rotates. The machine consists of very lightweight aluminum rods (they are so light that you can neglect their mass) connected to massive brackets with nets, 2 m from the center, that catch the baseball. The mass of each bracket at the end of a rod that holds a net is 10 kg. The entire machine sits on a low-friction axle fixed to the ground. When it catches a baseball, the machine's center of mass does not move. The machine's height is 1.0 m, and the ball travels nearly horizontally at the same height. The mass of the supporting rod is also negligible. See the pictures shown below.
A puck moving on ice with a speed 0.5 m/s collides with a puck that is attached to another puck via a very lightweight rigid rod, as shown in the figure below. Let's refer to the attached pucks as a "rotor." After the collision, the incoming puck rebounds backward with a speed of 0.1 m/s and the rotor moves to the right and rotates clockwise. Kinetic energy is not conserved during the collision. All pucks have the same mass of 0.1 kg and the length of the rod is 0.8 m. Neglect the mass of the rod.