A thin rod of mass m and length L is released from rest from a nearly upright position, let’s say θ = 89o. What is the minimum height from which the rod should be released in order to land horizontally when it hits the ground

A merry-go-round is a playground ride that consists of a large disk mounted to that it can freely rotate in a horizontal plane. The merry-go-round shown is initially at rest, has a radius R = 1.1 meters, and a mass M = 246 kg. A small boy of mass m = 46 kg runs tangentially to the merry-go-round at a speed of v = 1.9 m/s, and jumps on. 1.The boy then crawls to the center of the merry-go-round. What is the angular speed in radians/second of the merry-go-round when the boy is at the center of the merry go round?  2.Finally, the boy decides that he has had enough fun. He decides to crawl to the outer edge of the merry-go-round and jump off. Somehow, he manages to jump in such a way that he hits the ground with zero velocity with respect to the ground. What is the angular speed in radians/second of the merry-go-round after the boy jumps off?

A 1.10-kg particle moves in the xy plane with a velocity of v = (4.30 î –- 3.50 ĵ) m/s. Determine the angular momentum of the particle about the origin when its position vector is ŕ = (1.5o î + 2.20 ĵ) m. (0 î + 0 j + 13.85 Review the equation for the angular momentum in terms of components of the vectors. k) kg · mʻ/s

The figure shows a thin rod, of length L = 2.20 m and negligible mass, that can pivot about one end to rotate in a vertical circle. A heavy ball of mass m = 8.10 kg is attached to the other end. The rod is pulled aside to angle 00 = 8° and released with initial velocity V 0. (a) What is the speed of the ball at the lowest point? (b) Does the speed increase, decrease, or remain the same if %3D the mass is increased? 3.

A uniform rod is set up so that it can rotate about an axis at perpendicular to one of its ends. The length and mass of the rod are 0.801 m and 1.25 kg, respectively. A force of constant magnitude F acts on the rod at the end opposite the rotation axis. The direction of the force is perpendicular to both the rod's length and the rotation axis. Calculate the value of F that will accelerate the rod from rest to an angular speed of 6.49 rad/s in 8.61 s. F =

Calculate the magnitude of the cross product of the following two vectors: b = 2j + 5k = (0 ,2,5) å = 1î + 3ĵ = (1,3,0) , b= 2ĵ + 5k = (0 ,2 , 5)

A 3.0 kg particle moves in a circle of radius 2.0 m with an angular momentum of 30.0 kg⋅m2/s. What is its speed of rotation?

Consider three identical ramps with a height of 1 m. At the top of one ramp is a solid sphere. The second ramp has a hoop, and the third ramp has a solid cylinder. Assume each object has the same mass and radius. If the three objects are released simultaneously, in what order will they reach the end of their respective ramp? Rank them from first to last.

(a) Calculate the angular momentum (in kg • m2/s) of Neptune in its orbit around the Sun. (The mass of Neptune is 1.020 x 1026 kg, the orbital radius is 4.497 x 109 km and the orbital period is 165 y.) kg · m2/s (b) Compare this angular momentum with the angular momentum of Neptune on its axis. (The radius of Neptune is 2.476 x 104 km and the rotation period is 16.11 h.) Lorbital Lrotation

A 3.0 kg cylinder falls from rest through a distance of 6.0 m in an evacuated tube near the surface of the earth. What is its spee after the cylinder has fallen the 6.0 m distance?