Let's first find time that the basketball takes to stop:
ω=ω0+αt,t=−αω0=−−0.15 s2rad27 srad=180 s.
Then, we can find how many radians the basketball turns through:
θ=ω0t+21αt2,θ=27 srad⋅180 s+21⋅(−0.15 s2rad)⋅(180 s)2=2430 rad.Finally, we can find the number of revolutions that the basketball makes before coming to a stop:
Nrev=2430 rad⋅(2π rad1 rev)=387 rev.Answer:
Nrev=387 rev.
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