A thin rod of length 2L and mass M lies flat on a frictionless plane. It is not hinged (attached) to anything. A small ball of mass m, traveling with velocity Vo, strikes the rod at a distanceh from the rod's center of mass. The collision is elastic. The ball continues to move along the original line of motion after the collision. The rod moves on the plane and rotates around its center of mass. After the collision, we want to determine the rod translational velocity, the rod angular velocity and the ball final velocity. a) Write three equations to find these three unknowns based on m, M, L, h and vo. Do not try to solve the equations. b) If the collision were inelastic and the rod was hinged at its center CM, what would be the rotational angular velocity of the system after the collision? Top view m Yo L h CM M

The sphere of mass m1 = 5 kg falls from a height H = 1.4 m onto the homogeneous board of negligible mass. The board can rotate around a horizontal axis passing through point O, and a body of mass m2 = 3.9 kg is placed on it at a distance b = 1 m from the axis of rotation. The collision is perfectly inelastic. How high does the body of mass m2 rise after the collision (in m) if a = 0.5 m?

5 ELASTIC COLLISION A puck of mass 1.0 kg is moving on frictionless ice with a speed of 9.0 m/s. It has a collision with a puck 2.0 kg that is moving a speed of 6.0 m/s; the second puck is traveling at a 90⁰ relative to the first puck. Consider the first puck to be traveling along the f-axis in the pos- itive direction, and consider the second puck to be moving along the ŷ-axis in the negative direction. The pucks collide at the origin. What are the velocity vectors of the pucks after the collision?

A thin circular disk of radius R and mass M has an axle through it close to its outer edge. The disk is rotated through 90 deg and then allowed to drop.  (The figure shows the disk in its initial position before it is released, and its final position when point P passes through the lowest point). a) If the zero of height is taken to be the location of the COM when the disk is in its final position, what is the energy of the disk before it is release? b) What is the moment of inertia of the disk about the axle? c) What is the angular speed of the disk when it is in the final position? d) What is the speed of point P, on the outer edge of the disk, as it passes through the lowest point in its swing?

2. Fig. 2 shows a solid sphere of mass 2 kg and a massless string of total length 4 meters which is wrapped around the equator of the sphere (total length includes the length of wrapped string and the length of the string hanging from the ceiling). The sphere then falls vertically while rolling down (without slipping) the whole wrapped string and falls on top of an inclined plane. Due to the collision with the inclined plane, it loses all its kinetie energy within a very short time and starts rolling along the inclined plane with zero initial velocity. Consider that a total of 10 Joules of energy is lost during the motion of the sphere along the planes. The magnitude of gravitational acceleration g = 9.8 m/s². 1 m 3 m 2 m 30 Fig. 2 (a) Find the value of the moment of inertia of the sphere about its axis of rotation. (b) inclined plane? What is the magnitude of angular velocity of the sphere when it touches the (c) How far along the second inclined plane (45°) on the right will the…

In the figure, a solid cylinder of radius 12 cm and mass 14 kg starts from rest and rolls without slipping a distance L = 5.0 m down a roof that is inclined at angle 0 = 36°. After leaving the roof, the cylinder hits the ground at distance X = 4.1 m from the house. (a) What is the acceleration of the cylinder while it is rolling dowNn the roof? (b) What is the height H? (c) What are the magnitude and the direction of the velocity before the cylinder hits the ground?

. An object of mass 12 kg is suspended from a pulley which has a mass of 6 kg and a radius of rotation of 0.25 m. If at that time the pulley rotates with an angular velocity of 5 rad/s, we want to know that when the object moves down a distance of 2 m, then at what speed is the pulley rotating? If the friction force on the pulley bearing produces a moment of resistance of 2 N-m 12 kg 0.3 m

A 1.0-kg ball on the end of a string is whirled at a constant speed of 2.0 m/s in a horizontal circle of radius 1.5 m.  What is the work done by the centripetal force during one revolution?

The sphere of mass m1 = 5 kg falls from a height H = 1.4 m onto the homogeneous board of negligible mass. The board can rotate around a horizontal axis passing through point O, and a body of mass m2 = 3.9 kg is placed on it at a distance b = 1 m from the axis of rotation. The collision is perfectly inelastic. How high does the body of mass m2 rise after the collision (in m) if a = 0.5 m?

A steel ball of mass M is held at a distance H above a massless rigid tabletop supported by undamped springs whose equivalent stiffness is K. If the ball is left to fall from rest on the tabletop. Deduce an expression for the velocity at which the ball will bounce back off the tabletop. On its way back, will the mass bounce back to its initial height? If it will not, where will the difference in energy go? Discuss mathematically! (Pls solve the question in detail with figure)