Suppose a 180 kg motorcycle has two wheels and is heading toward a hill at a speed of 30.0 m/s. Assume the wheels to be approximately an annular ring with an inner radius of  R1 = 0.280 m  and an outer radius of  R2 = 0.440 m.  The mass of each wheel is 16.3 kg. (a) How high can it coast up the hill in meters, if you neglect friction? (Give your answer to at least 1 decimal place.)  m (b) How much energy, in joules, is lost to friction if the motorcycle only gains an altitude of 35.0 m before coming to rest?  J

A string is wrapped around a disk of mass m = 2.2 kg and radius R = 0.08 m. Starting from rest, you pull the string with a constant force F = 9 N along a nearly frictionless surface. At the instant when the center of the disk has moved a distance x = 0.12 m, your hand has moved a distance of d = 0.27 m. m d (a) At this instant, what is the speed of the center of mass of the disk? Vcm = m/s (b) At this instant, how much rotational kinetic energy does the disk have relative to its center of mass? Krot = Additional Materials M eBook

The figure shows a ball with mass m = 0.69 kg attached to the end of a thin rod with length L = 0.99 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?

Some European trucks run on energy stored in a rotating flywheel, with an electric motor getting the flywheel up to its top speed of 250 Trad/s. One such flywheel is a solid, uniform cylinder with a mass of 730 kg and a radius of 0.972 m. (a) What is the kinetic energy of the flywheel after charging? (b) If the truck uses an average power of 7.8 kW, for how many minutes can it operate between chargings? (a) Number (b) Number Units Units

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 solid ball with mass 9.10 kg and radius 2.00 cm is released from rest at the top of a ramp. The ramp is 4.20 m high and makes an angle of 12.0 degrees with the horizontal. The ball rolls down the ramp without slipping. (How do I use conservation of mechanical energy to find the speed of the ball at the bottom of the ramp?)

A jewel smith wishing to buff a finished piece of jewelry attaches a buffing disk to his drill. The radius of the disk is 4.10 mm, and he operates it at 2.25  104 rad/s. (a) Determine the tangential speed, in m/s, of the rim of the disk.  m/s (b) The jeweler increases the operating speed so that the tangential speed of the rim of the disk is now 285 m/s. What is the period of rotation, in seconds, of the disk now?  s

A uniform disk (1=1/2 mR2) has a mass of 3 kg and a radius of 2m. The disk is mounted on frictionless bearings and is used as a turntable. The turntable is initially rotating at 120 rpm (revolutions per minute, convert it to rad/s). A hollow cylinder has the same mass and radius as the disk. It is released from rest, just above the turntable, and on the same vertical axis. The hollow cylinder slips on the turntable for 0.20 s until it acquires the same final angular velocity as the turntable. (HINT: Note that some of the information given is not needed! Think which conservation law(s) apply.) The final angular momentum of the system is closest to: L = Submit [5] ΑΣΦ Request Answer ? kg. m²/s 4

Trucks can be run on energy stored in a rotating flywheel, with an electric motor getting the flywheel up to its top speed of 683 rad/s. One such flywheel is a solid, uniform cylinder with a mass of 535 kg and a radius of 1.2 m that rotates about its central axis. What is the kinetic energy of the flywheel after charging?  If the truck uses an average power of 8.4 kW, for how many minutes can it operate between chargings?