Define rotational kinetic energy of a body and obtain expression for it.
Answers
Explanation:
Answer is given above in the picture
Answer:
Rotational kinetic energy is the energy absorbed by the object by the virtue of its rotation.
Rotational kinetic energy = 1/2 (moment of inertia) (angular velocity)²
Explanation:
Rotational kinetic energy is equivalent to the work done by the torque. It can be used to determine the rotational kinetic energy of a rotating body.
Formula Derivation:
The net work done is equal to the force multiplied by the arc length travelled since the force is perpendicular to the displacement :
net W = (net F)Δs
Multiplying and Dividing RHS of equation by r :
net W = (r net F)Δs/r
since we know that r net F = net F(τ) and Δs/r = θ, thus
net W = (net τ)θ
now the torque is equivalent to force and angle is equivalent to distance . we remember that τ = Iα, means that
net W = Iαθ
with rotational kinetic equations
ω² = ω₀² + 2αθ
net W = 1/2 Iω² - 1/2 Iω₀²
The work-energy theorem only applies to rotational motion in this equation. As you may recall , a network alters a system's kinetic energy. We define the term : 1/2 Iω²
as rotational kinetic energy KE(rotational) for an object with a moment of inertia I and an angular velocity ω:
Rotational kinetic energy = 1/2 I ω²
where I = moment of inertia and ω = angular velocity .The expression for rotational kinetic energy is identical to that for transitional kinetic energy.