A solid ball (sphere) of mass 1 kg and radius 0.3 m is held at rest at the top of a ramp. There is enough friction so that the ball will roll down the ramp without slipping. The top of the ramp is 10 meters above the ground.What will the speed be of the ball just before it hits the bottom of the ramp?

A spring with spring constant k and equilibrium length zero is attached tothe top of a frictionless hoop of radius R. The spring is stretched and connected to a bead of mass m at the bottom of the hoop. At t = 0 the bead is given an initial speed v0 and the bead moves up the hoop. Find the speed of the bead as a function of position on hoop v(θ).

A 19 kg. rock is thrown straight down toward the Earth from a distance of 10 earth radii above the surface of the Earth with a speed of 5400 m/s. The radius of the Earth is 6370000 meters. The mass of the earth is 5.98e+24 kg. (A)Find the initial kinetic energy of the rock (in J)     (B)Find the initial potential energy (in J) of the rock (HINT: the "r" in the potential energy formula is measured from the CENTER of the Earth).     (C)Find the total initial energy (in J) of the rock     (D)What is the potential energy (in J) of the rock after it has fallen 4 Earth radii from its original position.     (E)Using the Conservation of Energy, find the speed (in m/s) of the rock after it has fallen 4 Earth radii from its original position.

A 24 g block sits at the center of a turntable that rotates at 80 rpm.  A compressed spring shoots the block radially outward from the center along a frictionless groove in the surface of the turntable.  Calculate the turntable's angular speed when the block reaches the outer edge.  Treat the turntable as a solid disk with mass with mass 200 g and diameter 54.0 cm.  Express your answer in revolutions per minute.

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 1500-kg satellite orbits a planet in a circular orbit of radius 6.2 × 106 m. What is the angular momentum, in kg m2/s, of the satellite in its orbit around the planet if the satellite completes one orbit every 1.5 × 104 s?

A box is being lowered from a height of 10m to the ground. A rope is attached to a cylinder. The cylinder is stationary and can be modeled as a solid disc and is 50kg with a radius of 0.8m. The cylinder is frictionless. The box has a mass of 80kg. If the box starts from rest, what is the speed right before it touches the ground?4

Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. A star with a of mass of 2.0x1032 kg and radius 7.0x108 m is initially rotating at a rate of once every 30 days. The star collapses into a neutron star with the same mass but a new radius of 16,000 m. What is the angular speed of the star? (Give your answer in rotations per second.) Assume the star is a solid sphere: Isphere = 2/5 MR2.   The Crab Nebula (shown below) formed from a nearby supernova (6000 light years away). Chinese astronomers observed the event in the year 1054 and since that time the nebula has been expanding into what it appears like today. The Crab Pulsar is a neutron star at the center of the nebula and the remains of the original supernova.

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?

The figure shows a ball with mass m = 2.0 kg attached to the end of a thin rod with length L = 0.79 m and negligible mass. The other end of the rod is pivoted so that the ball can move in a vertical circle. (a) What initial speed must be given the ball so that it reaches the vertically upward position with zero speed? What then is its speed at (b) the lowest point and (c) the point on the right at which the ball is level with the initial point? (d) If the ball's mass were doubled, what would the answer to (a) be?