# Rotational Energy conservation

• inner08
In summary, the total kinetic energy of a car with four wheels, each with a mass of 25kg and a radius of 30cm, and a car's mass of 1000kg, traveling at a speed of 30m/s neglecting friction, is 518kJ. To calculate the distance the car will travel up an incline of 10 degrees before stopping, one must use the equation mgxsin10 = 518000, where m is the mass of the car, g is the gravitational acceleration, x is the distance traveled, and 10 is the angle of the incline. This equation should yield a positive value for x, but if a negative value is obtained, it may
inner08
The four wheels of a car have each a mass of 25kg and a radius of 30cm. The car's mass is 1000kg. We neglect the losses due to friction. We assimilate the wheels to homogeneous cylinders.

a) What is the total kinetic energy of the car and the wheels if the speed of the car is 30m/s.

b) What distance will the car travel till it stops going up an incline of 10 degrees if the initial speed is of 30m/s?

For a I did,

Ktot = rotational kinetic energy + linear kinetic energy
= 1/2lw + 1/2mv^2
= (1/2)(4.5)(100)^2 + (1/2)(1100)(30)^2
= 518kJ

For b I thought I could just use "gravitational potential = rotational kinetic energy + linear kinetic energy"

h = xsin10
So mgx = rotational kinetic energy + linear kinetic energy
mgx = 518000
x = -89m

Obviously I did something wrong because I shouldn't be getting a minus...and on top of that I know the answer is 276m.

Any ideas on what I did wrong..or what I might of forgotten to do?

How do you go from mgx = 518000 to a negative answer for x? You are approaching it correctly using energies...

Sorry, that should read mgxsin10 = 518000

sin10 gives -0.544 therefore giving me a negative answer.

Any idea on what I might of done wrong?!

The sin of 10 degrees is not negative. Is your calculator in radian mode maybe?

Oh geez...lol..I didn't realize I was in radians...

Thanks

## 1. What is rotational energy conservation?

Rotational energy conservation is a physical law that states that the total amount of energy in a closed system remains constant over time. Specifically, it refers to the conservation of energy within a system that involves rotational motion, such as a spinning object.

## 2. How is rotational energy conserved?

Rotational energy is conserved through the principle of conservation of angular momentum. This states that the total angular momentum of a system remains constant, unless acted upon by an external torque. In other words, the rotational energy of a system can be transferred between objects within the system, but the total amount of energy remains constant.

## 3. What are some real-world examples of rotational energy conservation?

Some examples of rotational energy conservation in everyday life include the spinning of a top, the rotation of a merry-go-round, the movement of gears in a clock, and the spinning of a bicycle wheel. In all of these cases, the rotational energy is conserved unless acted upon by an external force.

## 4. How is rotational energy conservation related to other forms of energy conservation?

Rotational energy conservation is a specific application of the law of conservation of energy, which states that energy can neither be created nor destroyed, only transferred or transformed. This means that the total energy in a closed system, including both rotational and other forms of energy, remains constant.

## 5. Can rotational energy conservation be violated?

No, rotational energy conservation is a fundamental law of physics and cannot be violated. However, in certain situations, it may appear that rotational energy is being lost due to friction or other external forces. In reality, this energy is being transferred to other forms, such as heat or sound, and the total energy in the system remains constant.

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