**Rotational kinetic energy** (KE_{rotational}) is half the product of **rotational inertia **(I) and the square of **angular velocity** (ω). Using the formula of rotational kinetic energy: **KE**_{roatational}** = ½ × I ω**** ^{2}**, the value of rotational kinetic energy of an object can be calculated.

Let’s solve some problems based on this formula, so you’ll get a clear idea.

## Rotational Kinetic Energy Practice Problems

**Problem 1:** Calculate the rotational kinetic energy of an object which is having the moment of inertia of 2 kg m^{2} and is rotating with the 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

Using the formula of rotational kinetic energy,

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 the angular velocity of 15 rad/s and has the moment of inertia of 1 kg m^{2}. Calculate the rotational kinetic energy of a 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} = ?

Using the formula of rotational kinetic energy,

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 which has the moment of inertia of 30 kg m^{2} and is rotating with the 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

Using the formula of rotational kinetic energy,

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 the angular velocity of 8 rad/s. If a disc has the moment of inertia of 7 kg m^{2}, then calculate the rotational kinetic energy of a 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} = ?

Using the formula of rotational kinetic energy,

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**.

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**Related:**

- Thermal Energy Equation
- Potential Energy Formula
- Gravitational Potential Energy Formula
- Electric Potential Energy Formula
- Elastic Potential Energy Formula
- Kinetic Energy Formula
- Electrical Energy Equation
- Mechanical Energy Formula
- Photon Energy Equation
- Conservation of Energy Formula

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