Kinetic energy and the revolutions

[keweezz]

A car is designed to get its energy from a rotating flywheel with a radius of 1.90 m and a mass of 510.0 kg. Before a trip, the disk-shaped flywheel is attached to an electric motor, which brings the flywheel's rotational speed up to 1008.0 rev/min.

(a) Find the kinetic energy stored in the flywheel.
J
(b) If the flywheel is to supply as much energy to the car as a 7457 W motor would, find the length of time the car can run before the flywheel has to be brought back up to speed again.
s

trying to solve this problem is killing me.. Any hints or tips?

 

[Doc Al]

What have you tried so far? How do you calculate rotational KE?

 

[ogb p]

I would approach this problem by first understanding the concept of kinetic energy and its relationship to revolutions. Kinetic energy is the energy an object possesses due to its motion, and it is directly proportional to the mass and the square of the velocity of the object. In this case, the flywheel has a mass of 510.0 kg and a rotational speed of 1008.0 rev/min.

To find the kinetic energy stored in the flywheel, we can use the formula for rotational kinetic energy: E = 1/2 * I * ω^2, where E is the kinetic energy, I is the moment of inertia, and ω is the angular velocity. The moment of inertia for a disk-shaped flywheel is given by I = 1/2 * m * r^2, where m is the mass and r is the radius.

Plugging in the given values, we get E = 1/2 * (1/2 * 510.0 kg * (1.90 m)^2) * (1008.0 rev/min)^2. Converting the rotational speed to radians per second (ω = 1008.0 rev/min * 2π rad/rev * 1 min/60 s = 105.6 rad/s), we get E = 1.52 x 10^6 J. Therefore, the kinetic energy stored in the flywheel is 1.52 x 10^6 J.

Next, we need to find the length of time the car can run before the flywheel has to be brought back up to speed again. To do this, we can use the formula for work, W = ΔE, where W is the work done, ΔE is the change in energy, and E is the kinetic energy stored in the flywheel.

Since we want the flywheel to supply the same amount of energy as a 7457 W motor, we can set ΔE = 7457 J. Plugging in the value for E that we calculated earlier, we get W = 7457 J = 1.52 x 10^6 J - E. Solving for E, we get E = 1.52 x 10^6 J - 7457 J = 1.51 x 10^6 J.

Now, we can use the formula for rotational kinetic energy to find the angular velocity needed for the flywheel to supply