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Answer:
ac= 15.07 m/s²
Explanation:
The Wheel rotates with a constant angular acceleration.:
Centripetal acceleration is calculated as follows:
ac =ω² *R Formula (1)
ac =v² / R Formula (2)
Kinematics of the wheel
We apply the equations of circular motion uniformly accelerated :
ωf²= ω₀² + 2αθ Formula (3)
v = ω* R Formula (4)
Where:
θ : angle that the wheel has rotated in a given time interval (rad)
α : angular acceleration (rad/s²)
ω₀ : initial angular speed ( rad/s)
ωf : final angular speed ( rad/s)
v: tangential velocity of a point on the rim ( m/s)
R : radius of wheel (m)
ac: centripetal acceleration, (m/s²)
Data:
D = 40.0 cm : diameter of the wheel
R = D/2= 40.0 cm/ 2 = 20 cm = 0.2m
α = 3.00 rad/s^2
ω₀ = 0
n = 2 revolutions : number of revolutions
θ =2πn (rad) = 2π*2 (rad) = 4π rad
Calculate of the ωf
We replace data in the formula (3)
ωf²= ω₀² + 2αθ
ωf²= 0 + 2(3)(4π)
ωf²= 24π
ωf = 8.68 rad/s
Calculate of the v
We replace data in the formula (4)
v = ω*R
v = (8.68)*(0.2)
v = 1.736 m/s
Calculate of the ac
We replace data in the formula (1)
ac = ( ω)²*(R)
ac = (8.68)²*(0.2)
ac = 15.07 m/s²
We replace data in the formula (2)
ac = v²/ R
ac = ( 1.736 )²/(0.2)
ac = 15.07 m/s²