A fly wheel with radius 0.300 m starts from rest and accelerates with a constant angular acceleration of 0.600 rad/s2. For a point on the rim of the flying wheel, what are the magnitudes of the tangential, radial, and resultant accelerations and velocities after 2.00 seconds?
Solution) Radius , r = 0.300 m
wo = 0 ( rest)
Angular acceleration = 0.600 rad/s^2
t = 2.00 s
Tangential acceleration = ?
Tangential acceleration = r(angular acceleration)
Tangential acceleration = 0.300×0.600 = 0.180
Tangential acceleration, at = 0.180 m/s^2
Radial acceleration = ?
Radial acceleration = r(w^2)
w = wo + (angular acceleration)(t)
w = 0 + (0.600)(2.00)
w = 1.20 rad/s
Radial acceleration, ar = (0.300)(1.20^2)
ar = 0.432 m/s^2
Resultant acceleration , a = (at^2 + ar^2)^(1/2)
a = (0.180^2 + 0.432^2)^(1/2)
a = 0.468 m/s^2
Tangential velocity , Vt = ?
Vt = rw = 0.300×1.20 = 0.36 m/s
Radial velocity ,Vr = w = 1.20 rad/s
Resultant , V = (Vr^2 + Vt^2)^(1/2)
V = (1.20^2 + 0.36^2)^(1/2)
V = 1.25 m/s
A fly wheel with radius 0.300 m starts from rest and accelerates with a constant angular acceleration of 0.600 rad/s2
A Fly wheel with radius 0.300 m starts from rest and accelerates with a constant angular acceleration of 0.600 rad/s2. For a point on the rim of the flying wheel, what are the magnitudes of the tangential, radial, and resultant accelerations and velocities after 2.00 seconds?
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