Kinetic Energy in Rotational Motion Problem

In summary, the problem is to calculate the maximum amount of energy that can be stored in a flywheel with a radius of 1.30 m and a mass of 72.0 kg, given a maximum allowed radial acceleration of 3600 m/s^2. The solution involves solving for the angular velocity and moment of inertia, and plugging them into the rotational kinetic energy equation. However, the actual answer is half of the calculated value, which is due to the moment of inertia formula for a disk being (1/2)mr^2. Another similar problem is given with slightly different values, and a request for someone to solve it.
  • #1
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Ok the problem is:

Energy is to be stored in a flywheel in the shape of a uniform solid disk with a radius of 1.30 m and a mass of 72.0 kg. To prevent structural failure of the flywheel, the maximum allowed radial acceleration of a point on its rim is 3600 m/s^2.

What I did was solve for the angular velocity through the radial acceleration:

3600m/s^2 = rw^2

w = 52.6 rad/s

Then I solved for the moment of inertia:

I = mr^2 = 72.0kg(1.30m)^2 = 122 kg*m^2

Finally I plugged it all into the rotational kinetic energy equation:

K = (1/2)(122m*m^2)(52.6rad/s)^2 = 1.68*10^5 J

The actual answer is 8.42*10^4, exactly half of what I got. I don't suppose someone could explain where the *(1/2) is coming from?
 
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  • #2
The moment of inertia of a disk is?
 
  • #3
hehe (1/2)mr^2
 
  • #4
Energy is to be stored in a flywheel in the shape of a uniform solid disk with a radius of = 1.16m and a mass of 73.0 kg. To prevent structural failure of the flywheel, the maximum allowed radial acceleration of a point on its rim is 3510 m/s^2.

CAN SOMEONE PLEASE SOLVE THIS FFS IVE TRIED SO MANY OPTIONS AND ITS NOT WORKING!@@!_#!@#!@!@#)!@(#*)!@(#)((!@*
 

What is kinetic energy in rotational motion?

Kinetic energy in rotational motion is the energy an object possesses due to its rotation. It is calculated by the formula KE = 1/2 * I * ω^2, where I is the moment of inertia and ω is the angular velocity.

How is kinetic energy in rotational motion different from linear kinetic energy?

Kinetic energy in rotational motion is different from linear kinetic energy because it takes into account not only the mass and velocity of an object, but also its moment of inertia and angular velocity. In rotational motion, the object's shape and distribution of mass play a significant role in its kinetic energy.

What is the relationship between kinetic energy in rotational motion and torque?

The relationship between kinetic energy in rotational motion and torque is that torque, which is the rotational equivalent of force, is responsible for changing an object's angular velocity and therefore its kinetic energy. The greater the torque applied to an object, the greater its change in angular velocity and kinetic energy.

How does kinetic energy in rotational motion impact the stability of an object?

Kinetic energy in rotational motion can impact the stability of an object in several ways. If an object has a high rotational kinetic energy, it may be more difficult to control and keep in a stable position. Additionally, if an object's center of mass is not aligned with its axis of rotation, the object may experience wobbling or tipping, reducing its stability.

Can kinetic energy in rotational motion be converted into other forms of energy?

Yes, kinetic energy in rotational motion can be converted into other forms of energy, such as potential energy or thermal energy. For example, a spinning top has kinetic energy in rotational motion, but as it slows down and eventually stops, this energy is converted into potential energy due to its height above the ground. Frictional forces can also convert rotational kinetic energy into thermal energy.

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