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
Answer:
the angular acceleration = 205.706 rad/sec²
Step-by-step 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