Answer :
The wheel of diameter 3cm will take 16.35s to unwind the cord of length 4m with constant angular acceleration of 4rad/s².
=ω[tex]_{i}[/tex]t+ [tex]\frac{1}{2}[/tex] αt²
But ⍵[tex]_{i}[/tex] = 0
So, = [tex]\frac{1}{2}[/tex] αt² ----- (1)
= [tex]\frac{S}{r}[/tex] ;
S= 4m and r = [tex]\frac{3}{2}[/tex] = 1.5cm = 0.015m
= [tex]\frac{4}{0.015}[/tex] = 267 rad
Using this value of in eq. (1)
267 = [tex]\frac{1}{2}[/tex] × 2 × t²
t² = 267
t = [tex]\sqrt{267}[/tex]
t = 16.35s
Constant angular acceleration is when an object's angular velocity changes by the same amount in every equal time interval.
Acceleration is the rate of change of haste with respect to time.
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