A homogeneous disk with a mass of 3 kg and a radius of 20 cm, rotating with an angular velocity of 16π rad / s

A homogeneous disk with a mass of 3 kg and a radius of 20 cm, rotating with an angular velocity of 16π rad / s, begins to be decelerated by a tangential force of 0.05 N applied to its rim. How long does it take for the disc to stop?

m = 3 kg.

R = 20 cm = 0.2 m.

w0 = 16 * P rad / s.

w = 0 rad / s.

F = 0.05 N.

t -?

Let us write 2 Newton’s law for rotational motion: M = ε * I, where M is the moment of force, ε is the angular acceleration, I is the moment of inertia.

The angular acceleration ε is expressed by the formula: ε = (w – w0) / t. Since w = 0 rad / s, the formula will take the form: ε = – w0 / t. The sign “-” indicates that the angular acceleration ε is not corrected against the angular velocity w.

The moment of inertia I of a homogeneous disk is expressed by the formula: I = m * R ^ 2/2.

The moment of force is determined by the formula: M = F * R.

F * R = w0 * m * R ^ 2/2 * t.

F = w0 * m * R / 2 * t.

t = w0 * m * R / 2 * F.

t = 16 * 3.14 * 3 kg * 0.2 m / 2 * 0.05H = 301.5 s.

Answer: t = 301.5 s.