Question

A body having moment of inertia about its axis of rotation equal to 3 kg-m² is rotating with angular velocity equal to 3 rad/s. Kinetic energy of this rotating body is the same as that of a body of mass 27 kg moving with a speed of(a) 1.0 m/s(b) 0.5 m/s(c) 1.5 m/s(d) 2.0 m/s

Answer 1

Answer:

A)  1.0m/s

Explanation:

Rotation of the body = 3 kg-m² (Given)

Angular velocity of the body = 3 rad/s (Given)

Weight of the mass = 27kg (Given)

Using the equation of motion -

1/2Iω² = 1/2mv²

Therefore, 1/2.3kgm². 3²rad/s = 1/2.27kgv²

= 1/2.3kgm². 9rad/s = 1/2.27kgv²

Thus v² = 1

Thus, the kinetic energy of this rotating body is the same as that of a body of mass 27 kg moving with a speed of 1.0m/s.