# Rotational Kinetic Energy Formula | Problems And Solutions

Rotational kinetic energy (KErotational) is half the product of rotational inertia (I) and the square of angular velocity (ω). Using the formula of rotational kinetic energy: KEroatational = ½ × I ω2, 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 m2 and is rotating with the 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

Using the formula of rotational kinetic energy,
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 the angular velocity of 15 rad/s and has the moment of inertia of 1 kg m2. 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 m2
Rotational kinetic energy of a football, KErotational = ?

Using the formula of rotational kinetic energy,
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 which has the moment of inertia of 30 kg m2 and is rotating with the 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

Using the formula of rotational kinetic energy,
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 the angular velocity of 8 rad/s. If a disc has the moment of inertia of 7 kg m2, 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 m2
Rotational kinetic energy of a disc, KErotational = ?

Using the formula of rotational kinetic energy,
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.

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