Simple problems involving angular momentum

(Please express your answers in unit vector notation)

What is the gravitational force on the Earth due to the Sun at this moment?
What is the angular momentum of the Earth around the Sun at this moment?
What is the torque due to the Sun's gravitational force on the Earth?
In about 90 days, the Earth will move about one quarter of the way around the Sun in its orbit. What will its angular momentum around the Sun be at that time?

The Volvo corporation has recently designed a flywheel for its vehicles, which will store some of a car's kinetic energy as it slows at a red light:

Or see the version on Youtube

The center of the system is a spinning disk in the "Flywheel Module".

The wheel has

radius R = 10 cm
mass M = 5.9 kg
maximum angular velocity 60,000 RPM

What is the moment of inertia of the flywheel?
What is the maximum KE the wheel can store?
The Volvo SE sedan has a mass of 1600 kg. Suppose the sedan is rolling at 35 mph toward a red light. How much KE does the car have?
What fraction of this KE can be stored in the flywheel?

What is the maximum angular momentum of the flywheel?
Suppose that, as the car begins to drive again, the flywheel's angular momentum is transferred to the wheels over a duration of 3 seconds. What is the average torque delivered by the flywheel?
The Volvo SE sedan engine has a nominal torque of about 266 lb-ft = 360 N-m when it is over 1800 RPM. When the car is just staring to move, at, say, 1000 RPM, it might deliver half of that. How much of a boost is the flywheel?

Volvo's flywheel is still in the experimental phase, but it may reduce fuel consumption by a considerable amount in city driving. For more information about Volvo's flywheel, see