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The **rotational kinetic energy formula**, represented as KE_{rotational} = ½ × I ω^{2}, establishes a relationship between the rotational kinetic energy (KE_{rotational}) of an object, its rotational inertia (I), and the square of its angular velocity (ω). By using this formula, one can determine the amount of rotational kinetic energy possessed by an object based on its rotational inertia and the square of its angular velocity.

## Practice problems

### Problem #1

Calculate the rotational kinetic energy of an object with a moment of inertia of 2 kg m^{2}, rotating with an angular velocity of 4 rad/s.

**Solution**

Given data:

- Rotational kinetic energy of an object, KE
_{rotational}= ? - Moment of inertia of an object, I = 2 kg m
^{2} - Angular velocity of an object, ω = 4 rad/s

Applying the formula:

- KE
_{roatational}= ½ × I ω^{2} - KE
_{roatational}= ½ × 2 × (4)^{2} - KE
_{roatational}= 16 J

Therefore, the rotational kinetic energy of an object is **16 J**.

### Problem #2

A football is rotating with an angular velocity of 15 rad/s and has a moment of inertia of 1 kg m^{2}. Calculate the rotational kinetic energy of the football.

**Solution**

Given data:

- Angular velocity of a football, ω = 15 rad/s
- Moment of inertia of a football, I = 1 kg m
^{2} - Rotational kinetic energy of a football, KE
_{rotational}= ?

Applying the formula:

- KE
_{roatational}= ½ × I ω^{2} - KE
_{roatational}= ½ × 15 × (1)^{2} - KE
_{roatational}= 7.5 J

Therefore, the rotational kinetic energy of a football is **7.5 J**.

### Problem #3

What is the rotational kinetic energy of a sharpening wheel with a moment of inertia of 30 kg m^{2}, rotating with an angular velocity of 6 rad/s?

**Solution**

Given data:

- Rotational kinetic energy of a sharpening wheel, KE
_{rotational}= ? - Moment of inertia of a sharpening wheel, I = 30 kg m
^{2} - Angular velocity of a sharpening wheel, ω = 6 rad/s

Applying the formula:

- KE
_{roatational}= ½ × I ω^{2} - KE
_{roatational}= ½ × 30 × (6)^{2} - KE
_{roatational}= 15 × 36 - KE
_{roatational}= 540 J

Therefore, the rotational kinetic energy of a sharpening wheel is **540 J**.

### Problem #4

A disc placed in a DVD player rotates with an angular velocity of 8 rad/s. If the disc has a moment of inertia of 7 kg m^{2}, then calculate the rotational kinetic energy of the disc.

**Solution**

Given data:

- Angular velocity of a disc, ω = 8 rad/s
- Moment of inertia of a disc, I = 7 kg m
^{2} - Rotational kinetic energy of a disc, KE
_{rotational}= ?

Applying the formula:

- KE
_{roatational}= ½ × I ω^{2} - KE
_{roatational}= ½ × 7 × (8)^{2} - KE
_{roatational}= ½ × 7 ×64 - KE
_{rotational}= 7 × 32 - KE
_{roatational}= 224 J

Therefore, the rotational kinetic energy of a disc is **224 J**.

## Related

- Thermal energy equation
- Potential energy formula
- Gravitational potential energy formula
- Electric potential energy formula
- Elastic potential energy formula
- Kinetic energy formula
**Rotational kinetic energy formula**- Electrical energy equation
- Mechanical energy formula
- Photon energy equation
- Conservation of energy formula

## External links

- https://www.studysmarter.us/explanations/physics/engineering-physics/rotational-kinetic-energy/
- https://www.omnicalculator.com/physics/rotational-kinetic-energy
- https://study.com/skill/learn/how-to-calculate-the-rotational-kinetic-energy-from-inertia-explanation.html

Deep

Learnool.com was founded by Deep Rana, who is a mechanical engineer by profession and a blogger by passion. He has a good conceptual knowledge on different educational topics and he provides the same on this website. He loves to learn something new everyday and believes that the best utilization of free time is developing a new skill.