Flywheel energy for car The U.S. Department of Energy had...

Flywheel energy for car The U.S. Department of Energy had plans for a 1500-kg automobile to be powered completely by the rotational kinetic energy of a flywheel. (a) If the 300 -kg flywheel (included in the $1500-\mathrm{kg}$ mass of the automobile) had a $6.0-\mathrm{kg} \cdot \mathrm{m}^{2}$ rotational inertia and could turn at a maximum rotational speed of 3600 rad / s, determine the energy stored in the flywheel. (b) How many accelerations from a speed of zero to $15 \mathrm{m} / \mathrm{s}$ could the car make before the flywheel's energy was dissipated, assuming $100 \%$ energy transfer and no flywheel regeneration during braking? Ignore rotational kinetic energy of car wheels.

Key Concepts

Rotational Kinetic Energy

Rotational kinetic energy is the energy that an object possesses due to its rotation. It is given by the formula (1/2)I?², where I is the moment of inertia and ? is the angular velocity. This concept is essential when evaluating how much energy can be stored in rotating systems such as flywheels, which are used to store and transfer energy in various mechanical applications.

Moment of Inertia

The moment of inertia measures the resistance of a body to angular acceleration around a given axis and depends on the mass distribution relative to that axis. It is a key factor in determining the amount of energy a rotating system can store, as it directly affects the rotational kinetic energy alongside angular velocity.

Translational Kinetic Energy

Translational kinetic energy is the energy possessed by an object due to its linear motion and is calculated using the formula (1/2)mv², where m is the mass and v is the speed of the object. This concept is important when comparing the energy stored in a rotating system like a flywheel to the energy required to accelerate a vehicle, highlighting the energy conversion process between rotational and translational forms.

Energy Conversion and Transfer

Energy conversion involves transforming stored energy from one form to another, in this case from rotational kinetic energy to translational kinetic energy. The concept of energy conservation is employed, assuming ideal conditions with 100% efficiency, to calculate how many vehicle accelerations can be powered by the energy stored in the flywheel. This understanding is critical for applications in energy storage and utilization in automotive systems.

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