A disk with a rotational inertia of 5.0 kg .m² and a radius of 0.25 m rotates on a frictionless fixed axis perpendicular to the disk and through its center.A force of 8.0 N is applied tangentially to the rim.If the disk starts at rest, then after it has turned through half a revolution its angular velocity is: A)0.57 rad/s B)0.64 rad/s C)0.80 rad/s D)1.6 rad/s E)3.2 rad/s

Question

Quizplus · Accepted Answer

The work done by the force is equal to the change in kinetic energy. Work done = Force x distance = 8.0 N x (π x 0.25 m) = 2π J. The change in kinetic energy = 0.5 x I x ω^2, where I = 5.0 kg m^2. Solving for ω gives ω = sqrt((2 x 2π) / 5) = 1.6 rad/s.

A Disk with a Rotational Inertia of 5