rotating flywheel has been proposed as a means of temporarily storing mechanical energy in an automobile, providing an energy source for the car. The energy that can be stored in this way is limited by the size and weight of the flywheel and by the maximum angular velocity it can attain without flying apart. Suppose a solid cylindrical flywheel of radius 85.0cm and mass 80.0 kg rotates at a maximum angular velocity of 290 rad/s. Find the maximum rotational energy of the flywheel. How many liters of gasoline would provide the same mechanical energy given that each liter provides 8.50 106 J of mechanical energy? liters of gasoline

A metal can containing condensed mushroom soup has mass 230 g, height 10.6 cm and diameter 6.38 cm. It is placed at rest on its side at the top of a 3.00-m-long incline that is at 26.0° to the horizontal and is then released to roll straight down. It reaches the bottom of the incline after 1.50 s. (a) Assuming mechanical energy conservation, calculate the moment of inertia of the can. I = kg m m² · (b) Which pieces of data, if any, are unnecessary for calculating the solution? (Select all that apply.) the mass of the can the height of the can the angle of the incline the time the can takes to reach the bottom none of these 1 (c) Why can't the moment of inertia be calculated from I = 2 mr² mr2 for the cylindrical can?

In the figure, a wheel of radius 0.234 m is mounted on a frictionless horizontal axis. The rotational inertia of the wheel about the axis is 0.586 kg-m2. A massless cord wrapped around the wheel's circumference is attached to a 4.00 kg box. The system is released from rest.When the box has a kinetic energy of 4.00 J, what are (a) the wheel's rotational kinetic energy and (b) the distance the box has fallen? Assume free-fall acceleration to be equal to 9.81 m/s2. M (a) Number Units (b) Number Units

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 ball of mass M = 1.30 kg and radius r = 4.50 cm is attached to one end of a thin, cylindrical rod of length L = 14.0 cm and mass m = 0.880 kg. The ball and rod, initially at rest in a vertical position and free to rotate around the axis shown in the figure below, are nudged into motion. L m M (a) What is the rotational kinetic energy of the system when the ball and rod reach a horizontal position? J (b) What is the angular speed of the ball and rod when they reach a horizontal position? rad/s V(c) Vfreefall (c) What is the linear speed of the center of mass of the ball when the ball and rod reach a horizontal position? m/s (d) What is the ratio of the speed found in part (c) to the speed of a ball that falls freely through the same distance?

A car is designed to get its energy from a rotating flywheel in the shape of a uniform, solid disk of radius 0.650 m and mass 540 kg. Before a trip, the flywheel is attached to an electric motor, which brings the flywheel's rotational speed up to 5.30 ✕ 103 rev/min. HINT (a) Find the kinetic energy stored in the flywheel (in J).  J (b) If the flywheel is to supply energy to the car as a 12.5 hp motor would, find the length of time in hours the car could run before the flywheel would have to be brought back up to speed.

A metal can containing condensed mushroom soup has mass 230 g, height 11.0 cm and diameter 6.38 cm. It is placed at rest on its side at the top of a 3.00-m-long incline that is at 28.0° to the horizontal and is then released to roll straight down. It reaches the bottom of the incline after 1.50 s. (a) Assuming mechanical energy conservation, calculate the moment of inertia of the can. I = kg · m2 (b) Which pieces of data, if any, are unnecessary for calculating the solution? (Select all that apply.) O the mass of the can the height of the can O the angle of the incline O the time the can takes to reach the bottom O none of these (c) Why can't the moment of inertia be calculated from I = mr2 for the cylindrical can?

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?