Rotational Kinetic Energy:

The formula for rotational kinetic energy is given by:

K.E. = (1/2) I ω²

where K.E. is the rotational kinetic energy, I is the moment of inertia, and ω is the angular velocity.

To find the rotational kinetic energy, we need to find the moment of inertia (I) and the angular velocity (ω).

Moment of Inertia:

The moment of inertia (I) depends on the mass of the object and its distribution around the axis of rotation. For a body rotating in a circular path, the moment of inertia can be calculated using the formula:

I = (1/4) m r²

where m is the mass of the body and r is the radius of the circular path.

Given:
Mass (m) = 20 kg
Diameter (d) = 0.2 m

The radius (r) can be calculated by dividing the diameter by 2:
r = d/2 = 0.2/2 = 0.1 m

Substituting the values in the formula, we get:
I = (1/4) (20 kg) (0.1 m)²
I = (1/4) (20 kg) (0.01 m²)
I = 0.05 kg m²

Angular Velocity:

The angular velocity (ω) is given by the formula:

ω = 2π f

where ω is the angular velocity and f is the frequency of rotation in revolutions per second.

Given:
Frequency (f) = 100 revolutions/3 seconds

The angular velocity can be calculated by multiplying the frequency by 2π:
ω = 2π (100/3) rad/s
ω = 200π/3 rad/s

Calculating Rotational Kinetic Energy:

Now that we have the moment of inertia (I) and the angular velocity (ω), we can calculate the rotational kinetic energy (K.E.) using the formula:

K.E. = (1/2) I ω²

Substituting the values, we get:
K.E. = (1/2) (0.05 kg m²) (200π/3 rad/s)²
K.E. = (1/2) (0.05 kg m²) (40000π²/9) J
K.E. = (0.05 kg m²) (20000π²/9) J
K.E. ≈ 3495.8 J

Therefore, the rotational kinetic energy of the body is approximately 3495.8 Joules.

Angular Momentum:

The formula for angular momentum (L) is given by:

L = I ω

where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

To find the angular momentum, we need to use the moment of inertia (I) and the angular velocity (ω) calculated earlier.

Substituting the values, we get:
L = (0.05 kg m²) (200π/3 rad/s)
L ≈ 104.7 kg m²/s

Therefore, the angular momentum of the body is approximately 104.7 kg m²/s.