A 4.00-m length of light nylon cord is wound around a uniform cylindrical spool

Question

A 4.00-m length of light nylon cord is wound around a uniform cylindrical spool of radius 0.500 m and mass 1.00 kg. The spool is mounted on a frictionless axle and is initially at rest. The cord is pulled from the spool with a constant acceleration of magnitude 2.90 m/s2.

(a) How much work has been done on the spool when it reaches an angular speed of 7.35 rad/s?
Ans:3.376 J (is correct)

(b) How long does it take the spool to reach this angular speed?
Ans:1.2758 s (is correct)

(c) How much cord is left on the spool when it reaches this angular speed?
Ans: ???? (I need this answer)

Explanation / Answer

c) the legth of the cord leaving the spool, l = 0.5*a*t^2 (using kinematic equation)

= 0.5*2.9*1.2758^2

= 2.36 m

the length of the cord left on the spool = 4 - 2.36

= 1.64 m

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