A cord is wrapped around the outer surface of the 8-kg disk. If a force of F = (1⁄4u2) N, where u is in radians, is applied to the cord, determine the disk’s angular acceleration when it has turned 5 revol

A cord is wrapped around the outer surface of the 8-kg disk. If a force of F = (1⁄4θ²) N, where θ is in radians, is applied to the cord, determine the disk’s angular acceleration when it has turned 5 revolutions. The disc has an initial angular velocity and radius from the center of the disc = 300 mm

the angular acceleration = 205.706 rad/sec²

Explanation:

GIVEN THAT:

The disc mass = 8 kg

Force =

We are told that the given θ is in radians; Therefore; the when it has turned 5 revolutions; we have the θ to be:

Also;

the initial angular velocity

radius from the center of the disc = 300 mm = 0.3 m

Thus; the mass moment about the Inertia can be determined via the following expression;

Now to calculate the angular acceleration; we equate the sum of the moments acting on the Inertia;

SO:

Hence; the angular acceleration = 205.706 rad/sec²