The disc rotates uniformly around its axis. The speed of a point located at a distance of 30 cm

The disc rotates uniformly around its axis. The speed of a point located at a distance of 30 cm from the center of the disk is 1.5 m / s. The speed of the extreme points of the disk is 2m / s. Determine the radius of the disc.

The speed v of the points of the disk, evenly rotating around its axis, is related to its distance r from the center by the formula: v = (2 ∙ π ∙ r): Т, where Т is the time of one complete revolution or the period of rotation of the disk, the coefficient π ≈ 3.14 … Then:

Т = (2 ∙ π ∙ r): v.

From the condition of the problem it is known that the speed of a point located at a distance of r = 30 cm = 0.3 m from the center of the disk is v₁ = 1.5 m / s, we get: T = (2 ∙ π ∙ r): v₁. The speed v₂ of the extreme points of the disk is v₂ = 2 m / s, which means: T = (2 ∙ π ∙ R): v₂. Hence:

(2 ∙ π ∙ r): v₁ = (2 ∙ π ∙ R): v₂ or

R = (v₂ ∙ r): v₁, where R is the radius of the disk.

Substitute the values ​​of the quantities into the calculation formula:

R = (2 m / s ∙ 0.3 m): 1.5 m / s;

R = 0.4 m.

Answer: The radius of the disc is 0.4 meters.