the speed of a moving car is 60km/h . The wheels having diameter 0.60m are stopped in 10 rotations by applying brakes what will be angular retardation after applying the brakes
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Explanation:
Given speed of the vehicle=72㎞/hr
=72×
18
5
=20m/s
radius of the wheel =
2
0.5
=0.25
initial angular velocity (ω
0
)=
0.25
20
=80rad/s
angle covered after applying brakes=20×2π=40π
let the angular retardation be −αrad/s
2
final angular momentum ω=0
putting formula ω
2
=ω
0
2
−2αθ
⇒0=ω
0
2
−2×α×θ
⇒ω
0
2
=2×α×θ
⇒80
2
=2×α×40×π
⇒α=
80×π
80
2
⇒α=
π
80
putting the value of π=3.14
α=25.47rad/s
2
so retardation is −25.477≅−25.5 rad/s
2
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