Question

A cord is wrapped around a spool with radius 20 cm. The spool is free to rotate about an axle that lies along the x-axis in some coordinate system. The cord is pulled without slipping in the +y direction with velocity v = v_0 + k_0t^2, where v_0 = 5 cm/s and k_0 = 0.1 cm/s^3. Using vector notation, compute the angular velocity and angular acceleration of the spool.

Answer 1

here,

radius of the spool , r = 0.2 m

v = v0 + k0 * t^2

v0 = 0.05 m/s

k0 = 0.001 m/s^3

the angular velocity , w = v/r

w = (v0 + k0 * t^2)/r

and

differentiating the equation of angular accelration

angular accelration , alpha = ( 0 + 2 * k0 * t ) /r

alpha = 2 * k0 * t /r