It has been argued that power plants should make use of off-peak hours (such as late at night) to generate mechanical energy and store it until it is needed during peak load times, such as the middle of the day. One suggestion has been to store the energy in large flywheels spinning on nearly frictionless ball bearings. Consider a flywheel made of iron (density 7800 kg/m 3 ) in the shape of a 10.0-cm-thick uniform disk. (a) What would the diameter of such a disk need to be if it is to store 10.0 megajoules of kinetic energy when spinning at 90.0 rpm about an axis perpendicular to the disk at its center? (b) What would be the centripetal acceleration of a point on its rim when spinning at this rate?
It has been argued that power plants should make use of off-peak hours (such as late at night) to generate mechanical energy and store it until it is needed during peak load times, such as the middle of the day. One suggestion has been to store the energy in large flywheels spinning on nearly frictionless ball bearings. Consider a flywheel made of iron (density 7800 kg/m 3 ) in the shape of a 10.0-cm-thick uniform disk. (a) What would the diameter of such a disk need to be if it is to store 10.0 megajoules of kinetic energy when spinning at 90.0 rpm about an axis perpendicular to the disk at its center? (b) What would be the centripetal acceleration of a point on its rim when spinning at this rate?
It has been argued that power plants should make use of off-peak hours (such as late at night) to generate mechanical energy and store it until it is needed during peak load times, such as the middle of the day. One suggestion has been to store the energy in large flywheels spinning on nearly frictionless ball bearings. Consider a flywheel made of iron (density 7800 kg/m3) in the shape of a 10.0-cm-thick uniform disk. (a) What would the diameter of such a disk need to be if it is to store 10.0 megajoules of kinetic energy when spinning at 90.0 rpm about an axis perpendicular to the disk at its center? (b) What would be the centripetal acceleration of a point on its rim when spinning at this rate?
When the electricity goes out on your campus, a backup source powers the servers that handle communications and the Internet. Rather than use batteries, many installations use a flywheel, a heavy rotating disk that spins, very rapidly, with nearly zero friction. An electric motor spins up the flywheel, which continues to spin with very little energy input. When the system needs to provide power, the flywheel’s motion is used to turn an electric generator. A typical system has a 540 kg cylinder with a radius of 0.30 m. A small electric motor provides a constant 2.8 N ⋅ m torque to spin up the cylinder. If the cylinder starts at rest, how long does it take to reach its final spin rate of 13,000 rpm?
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?
A 330 kg motorcycle includes two wheels, each of which is 48 cm in diameter and has rotational inertia 2.5 kg⋅m2 . The cycle and its 61 kg rider are coasting at 90 km/h on a flat road when they encounter a hill. If the cycle rolls up the hill with no applied power and no significant internal friction, what vertical height will it reach?
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