A cylinder with a diameter of 16 cm rolls with an angular speed of 0.50 rad/s on a level surface.?

Question

A cylinder with a diameter of 16 cm rolls with an angular speed of 0.50 rad/s on a level surface. If the cylinder experiences a uniform tangential acceleration of 0.018 m/s2 without slipping until its angular speed is 1.04 rad/s, through how many complete revolutions does the cylinder rotate during the time it accelerates?

---------rotations

Answer 1

Let:

a be the angular acceleration,

u be the initial angular velocity,

v be the final angular velocity,

s be the angle turned.

a = 0.018 / 0.08 rad/s^2

v^2 = u^2 + 2as

s = (v^2 - u^2) / (2a)

= (1.04^2 - 0.50^2) / (2 * 0.018 / 0.08) rad

= (1.04^2 - 0.50^2) / (4pi * 0.018  / 0.08) rev

= 0.294 rev.