# Rotational kinetic energy formula

The rotational kinetic energy formula, represented as KErotational = ½ × I ω2, establishes a relationship between the rotational kinetic energy (KErotational) 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.

Contents

## Practice problems

### Problem #1

Calculate the rotational kinetic energy of an object with a moment of inertia of 2 kg m2, rotating with an angular velocity of 4 rad/s.

Solution

Given data:

• Rotational kinetic energy of an object, KErotational = ?
• Moment of inertia of an object, I = 2 kg m2
• Angular velocity of an object, ω = 4 rad/s

Applying the formula:

• KEroatational = ½ × I ω2
• KEroatational = ½ × 2 × (4)2
• KEroatational = 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 m2. 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 m2
• Rotational kinetic energy of a football, KErotational = ?

Applying the formula:

• KEroatational = ½ × I ω2
• KEroatational = ½ × 15 × (1)2
• KEroatational = 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 m2, rotating with an angular velocity of 6 rad/s?

Solution

Given data:

• Rotational kinetic energy of a sharpening wheel, KErotational = ?
• Moment of inertia of a sharpening wheel, I = 30 kg m2
• Angular velocity of a sharpening wheel, ω = 6 rad/s

Applying the formula:

• KEroatational = ½ × I ω2
• KEroatational = ½ × 30 × (6)2
• KEroatational = 15 × 36
• KEroatational = 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 m2, 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 m2
• Rotational kinetic energy of a disc, KErotational = ?

Applying the formula:

• KEroatational = ½ × I ω2
• KEroatational = ½ × 7 × (8)2
• KEroatational = ½ × 7 ×64
• KErotational = 7 × 32
• KEroatational = 224 J

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