What is the kinetic energy of a 120-cm thin uniform rod with a mass of 450 g that is rotating about its center at 3.60 rad/s?

Kinetic Energy: This is the energy possessed by a body due to its motion. The S.I unit of kinetic energy is Joules (J). The formula of kinetic energy is given as

Ek = 1/2mv²................. Equation 1

Where Ek = kinetic energy, m = mass of the uniform rod, v = liner velocity of the rod.

But,

v = αr .......................... Equation 2

Where α = angular velocity of the rod, r = radius of the circle.

Given: α = 3.6 red/s, r = 120/2 = 60 cm = 0.6 m.

Substitute into equation 2

v = 3.6(0.6)

v = 2.16 m/s.

Also given: m = 450 g = 0.45 kg.

Substitute into equation 1

Ek = 1/2(0.45)(2.16²)

Ek = 1.05 J.

raphealnwobi raphealnwobi · Answer 2 · 2021-12-14T10:41:07+01:00

The kinetic energy of a 120-cm thin uniform rod is 0.35 J

Kinetic energy is the energy stored in an object as a result of the its motion.

Kinetic energy (KE) is given by:

KE = (1/2)Iω²

I is the moment of inertia and ω is the angular velocity.

Given that ω = 3.6 rad/s, mass (M) = 450g = 0.45 kg, length (L) = 120cm = 1.2 m

I = ML²/12 = 0.45(1.2)² / 12 = 0.054 kg.m²

KE = (1/2)Iω²

KE = (1/2) * 0.054 * 3.6² = 0.35 J

The kinetic energy of a 120-cm thin uniform rod is 0.35 J

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