Question Detail
Question
For a rigid body rotating with angular frequency ω, the total kinetic energy is the sum of the kinetic energies of its constituent particles. This sum can be expressed as Σ (1/2) m_i v_i². What is the correct simplification of this expression using angular velocity?
Correct Answer
Option C is the correct answer.
Detailed Explanation
For a rigid body rotating with angular frequency ω, the linear speed of a particle i at a distance r_i from the axis is v_i = ω r_i. Substituting this into the kinetic energy expression gives KE = Σ (1/2) m_i (ω r_i)² = Σ (1/2) m_i ω² r_i².
Hint
Relate the linear velocity of a particle in a rotating rigid body to its angular velocity and distance from the axis.