# What Is the Correct Angular Speed for Doubling the CD's Kinetic Energy?

• UCrazyBeautifulU
In summary, the kinetic energy of a rotating rigid body is given by the formula 1/2 * m * (r * ω)^2. To double the kinetic energy, the angular speed must be increased by (√2). However, the formula used did not take into account the varying linear speed based on the radius, so the correct moment of inertia for the CD must be used in the formula.
UCrazyBeautifulU
A 10.7 g CD with a radius of 6.06 cm rotates with an angular speed of 30.9 rad/s. What is its kinetic energy?

What angular speed must the CD have if its kinetic energy is to be doubled? Here is my work:

kinetic energy energy = 1/2 m v2
= 1/2 m ( r ω )2
= 0.5 x 0.0107 x ( 0.0606 x 30.9 )^2 J

angular speed must be increased by ( 2)^ 1/2 if kinetic energy is duobled
since kinetice enrgy is proportional to ω2

That answer isn't right, it comes out to be 0.188 J, can anyone tell me what is wrong with my equation?

UCrazyBeautifulU said:
A 10.7 g CD with a radius of 6.06 cm rotates with an angular speed of 30.9 rad/s. What is its kinetic energy?

What angular speed must the CD have if its kinetic energy is to be doubled?

Here is my work:

kinetic energy energy = 1/2 m v2
= 1/2 m ( r ω )2
= 0.5 x 0.0107 x ( 0.0606 x 30.9 )^2 J

angular speed must be increased by ( 2)^ 1/2 if kinetic energy is duobled
since kinetice enrgy is proportional to ω2

That answer isn't right, it comes out to be 0.188 J, can anyone tell me what is wrong with my equation?
Chek your formula for the kinetic energy of a rotating rigid body. Not everything is moving with the speed you used.

what is wrong with the formula? Only one speed is given.

See this for discussion of rotational kinetic energy.

http://hyperphysics.phy-astr.gsu.edu/hbase/rke.html

One angular speed is given, but the local linear speed depends on r to which OlderDan alluded, i.e. v = $\omega$r.

One must use the appropriate moment of inertia for the CD.

Thanks for all the wonderful help!

## 1. What is rotational kinematics?

Rotational kinematics is the branch of physics that studies the motion of objects that are rotating around an axis. It involves the measurement and analysis of rotational quantities such as angular position, velocity, and acceleration.

## 2. How is rotational kinematics different from linear kinematics?

Rotational kinematics deals with the motion of objects that are rotating, while linear kinematics focuses on the motion of objects in a straight line. Rotational kinematics also involves the use of angular measurements and quantities, while linear kinematics uses linear measurements and quantities.

## 3. What is rotational energy?

Rotational energy is the energy possessed by an object due to its rotational motion. It is a form of kinetic energy and is dependent on the object's moment of inertia (a measure of its resistance to rotation) and its angular velocity.

## 4. How is rotational energy related to linear energy?

Rotational energy and linear energy are both forms of kinetic energy, and they are related through the concept of rotational inertia. Rotational inertia is the rotational equivalent of mass in linear motion, and it determines the relationship between an object's rotational energy and its linear energy.

## 5. What is the relationship between torque and rotational motion?

Torque is a measure of the force that causes an object to rotate around an axis. It is directly related to an object's rotational motion, as a greater torque will result in a greater acceleration of rotational motion. In other words, torque is the rotational equivalent of force in linear motion.

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