# What is translational kinetic energy?

An object that has motion - whether it is vertical or horizontal motion - has

**kinetic energy**. There are many forms of**kinetic energy**- vibrational (the**energy**due to vibrational motion), rotational (the**energy**due to rotational motion), and**translational**(the**energy**due to motion from one location to another).A.

### What is the formula for rotational kinetic energy?

The

**angular**acceleration is equal to the final**angular**velocity divided by the time and the average**angular**velocity is equal to half the final**angular**velocity. It follows that the**rotational kinetic energy**given to the flywheel is equal to the work done by the torque. Rolling objects. Index. Moment of inertia#### What is the rotational kinetic energy of the system?

As the Earth has a period of about 23.93 hours, it has an angular velocity of 7.29×10^{−}^{5}rad/s. The Earth has a moment of inertia, I = 8.04×10^{37}kg. m^{2}. Therefore, it has a rotational kinetic energy of**2.138**×10.^{29}J#### What is the formula for rotational inertia?

**Rotational inertia**is a property of any object which can be rotated. It is a scalar value which tells us how difficult it is to change the**rotational**velocity of the object around a given**rotational**axis.**Rotational inertia**plays a similar role in**rotational**mechanics to mass in linear mechanics.#### What is the unit of angular velocity?

This speed can be measured in the**SI unit**of angular velocity,**radians**per**second**, or in terms of degrees per**second**, degrees per hour, etc. Angular velocity is usually represented by the**symbol omega**(ω, rarely Ω).

B.

### Is kinetic energy conserved in rotation?

Just as in translational

**motion**(where**kinetic energy**equals 1/2mv^{2}where m is mass and v is velocity ),**energy**is**conserved in rotational motion**.**Kinetic energy**(K.E.) in**rotational motion**is related to moment of**rotational**inertia (I) and angular velocity (ω):#### Why does a ballerina spin faster when she pulls her arms in?

Example: Figure Skater**Spins**. When a figure skater draws**her arms**and a leg inward,**she**reduces the distance between the axis of rotation and some of**her**mass, reducing**her**moment of inertia. Since angular momentum**is**conserved,**her**rotational velocity must increase to compensate.#### What is the formula for rotational kinetic energy?

The**angular**acceleration is equal to the final**angular**velocity divided by the time and the average**angular**velocity is equal to half the final**angular**velocity. It follows that the**rotational kinetic energy**given to the flywheel is equal to the work done by the torque. Rolling objects. Index. Moment of inertia#### How do you know if angular momentum is conserved?

The symbol for**angular momentum**is the letter L. Just as linear**momentum is conserved when**there is no net external forces,**angular momentum**is constant or**conserved when**the net torque is zero.

C.

### Can rotational kinetic energy be negative?

If the object is rotating clockwise and the torque is a clockwise torque, the work is positive; a counter-clockwise torque applied to a clockwise rotating object

**does negative**work. A spinning object has**rotational kinetic energy**: A rolling object has both translational and**rotational kinetic energy**.#### Can kinetic energy ever be negative?

Since**kinetic energy**is based on motion, it is always a positive value. If it is not in motion, the**kinetic energy**of that object is zero.**Kinetic energy can**never be a**negative**value.**Kinetic energy can**be quantified as one half of the mass times the velocity squared (KE =^{1}/_{2}*m*v²).#### Is kinetic energy conserved in rotation?

Just as in translational**motion**(where**kinetic energy**equals 1/2mv^{2}where m is mass and v is velocity ),**energy**is**conserved in rotational motion**.**Kinetic energy**(K.E.) in**rotational motion**is related to moment of**rotational**inertia (I) and angular velocity (ω):#### What is rotational kinetic energy measured in?

As the Earth has a period of about 23.93 hours, it has an angular velocity of**7.29×10**^{−}^{5}rad/s. The Earth has a moment of inertia, I =**8.04×10**^{37}kg. m^{2}. Therefore, it has a rotational kinetic energy of 2.138×10^{29}J.

Updated: 21st September 2018