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One possibility for a low-pollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1100 $\mathrm{kg}$ uses a uniform cylindrical flywheel of diameter 1.50 $\mathrm{m}$ and mass $240 \mathrm{kg},$ and should be able to travel 350 $\mathrm{km}$ without needing a flywheel "spinup." (a) Make reasonable assumptions (average frictional retarding force $=450 \mathrm{N},$ twenty acceleration periods from rest to $95 \mathrm{km} / \mathrm{h},$ equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and estimate what total energy needs to be stored in the flywheel. (b) What is the angular velocity of the flywheel when it has a full "energy charge"? (c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip?

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(a) $1.7 \times 10^{8} J$(b) 2200 $\mathrm{rad} / \mathrm{s}$(c) 25 $\mathrm{min}$

Physics 101 Mechanics

Chapter 10

Rotational Motion

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Rutgers, The State University of New Jersey

Hope College

University of Winnipeg

Lectures

02:21

In physics, rotational dynamics is the study of the kinematics and kinetics of rotational motion, the motion of rigid bodies, and the about axes of the body. It can be divided into the study of torque and the study of angular velocity.

02:34

In physics, a rigid body is an object that is not deformed by the stress of external forces. The term "rigid body" is used in the context of classical mechanics, where it refers to a body that has no degrees of freedom and is completely described by its position and the forces applied to it. A rigid body is a special case of a solid body, and is one type of spatial body. The term "rigid body" is also used in the context of continuum mechanics, where it refers to a solid body that is deformed by external forces, but does not change in volume. In continuum mechanics, a rigid body is a continuous body that has no internal degrees of freedom. The term "rigid body" is also used in the context of quantum mechanics, where it refers to a body that cannot be squeezed into a smaller volume without changing its shape.

02:12

One possibility for a low-…

01:42

A car is designed to get i…

01:34

Flywheel energy for car Th…

05:13

02:41

An experimental flywheel, …

02:03

08:12

01:50

A car is fitted with an en…

01:39

A flywheel is a solid disk…

01:31

In a city with an air-poll…

the initial energy of the flywheel is used for two purposes one to give the car translational kinetic energy 20 times And then to replace the energy lost of friction from a resistance and from breaking. So we consider the work of friction is gonna be equaling the final kinetic energy minus the initial kinetic energy. And so we have the force of friction times the displacement in the extraction times co sign of 180 degrees. We know that this is gonna equal negative one. This would be equal to 1/2 times the mass of the car times the velocity of the car squared minus the kinetic energy of the fly Real. We can then say that the kinetic energy of the flywheel we know to be the force of friction times the changing times, changing displacement in the ex direction plus 1/2 times the mass of the car times the velocity of the car squared. This is gonna be equaling. 450 Newtons multiplied by 3.5 times 10 to the fifth meters and then plus 20 multiplied by 1/2 times the mass of the car. 1100 kilograms times this should be 95 kilometers per hour, multiplied by one meter per second for every no, that's not get a new line again. 95 kilometers per our multiplied by one meter per second for every 3.6 kilometers per hour Quantity squared and we find that the kinetic energy of the flywheel is gonna is equal in 1.65 times 10 to the eighth. Jules, this would be our answer four per day for the kinetic energy of the flywheel four part B. We can say that the kinetic energy of the flywheel is equaling the rotational kinetic, the rotational kinetic energy 1/2 times the moment of inertia times the angular velocity squared. And so the angular velocity would simply be equal to the square root. Uh, time square root of two times the kinetic energy divided by the moment of inertia. I And so this would be the square root of two times 1.652 will round at the very end times 10 to the eighth Jules. And then this would be divided by 1/2 times the mass of 140 kilograms. Times 0.75 meters quantity squared and we find that the angular velocity is 2200. Radiance curse. Second, this would be our answer for part B for Part C. Then, to find time, we're going to use the relationship. That power is equaling the work over the time. And so here the time would be equally the work done by the motor divided by the power. And so this is equaling the work done by the motor, which is equaling the kinetic energy of the flywheel again. 1.652 times, 10 to the eighth jewels. And then this would be divided by 150 horsepower. And then there are 746 watts for every one horsepower. And so T is equaling 1.48 times 10 to the third seconds. This would be your answer for part C. That is the end of the solution. Thank you for

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