Question

A coin with a diameter of 2.40 cm is dropped on edge onto a horizontal surface. The coin starts out with an initial angular speed of 18.0 rad/s and rolls in a straight line without slipping. If the rotation slows with an angular acceleration of magnitude 1.90 rad/s2, how far does the coin roll before coming to rest

Answer 1

Answer:

The coin comes to rest after covering 1.023 m.

Explanation:

initial angular speed, wo = 18 rad/s

final angular speed, w = 0 rad/s

angular acceleration, = 1.9 rad/s2

radius, r = 1.2 cm =  0.012 m

initial linear velocity, u = r wo = 0.012 x 18 = 0.216 m/s

final linear speed, v = r w = 0.012 x 0 = 0 m/s

linear acceleration, a = r x angular acceleration = 0.012 x 1.9 = 0.0228 m/s2

let the distance traveled is s.

Use third equation of motion

$v^{2} = u^{2} + 2 a s\\0 = 0.216^{2} - 2 \times 0.0228\times s\\s = 1.023 m$