A flywheel with a radius of 0.300 m starts from rest and accelerates with a constant angular acceleration of 0.200 rad/s2 .
(a) Compute the magnitude of the resultant acceleration of a point on its rim after it has turned through 60.0 degrees.
(b) Compute the magnitude of the radial acceleration of a point on its rim after it has turned through 120.0 degrees.
Radius of the flywheel = R = 0.3 m
Initial angular speed of the flywheel = 1 = 0 rad/s
Angular acceleration of the flywheel = = 0.2 rad/s2
Angle through which the flywheel has turned = 1 = 60 deg = 60 x (2/360) rad = 1.0472 rad
Angular speed of the flywheel after it has turned through 60 degrees = 2
22 = 12 + 21
22 = (0)2 + (2)(0.2)(1.0472)
2 = 0.6472 rad/s
Radial acceleration of a point at the rim after the flywheel has turned through 60 degrees = a1r
a1r = 22R
a1r = (0.6472)2(0.3)
a1r = 0.12566 m/s2
Tangential acceleration of a point at the rim after the flywheel has turned through 60 degrees = a1t
a1t = R
a1t = (0.2)(0.3)
a1t = 0.06 m/s2
Resultant acceleration of a point at the rim after the flywheel has turned through 60 degrees = a1
a1 = 0.139 m/s2
Angle through which the flywheel has turned = 2 = 120 deg = 120 x (2/360) rad = 2.0944 rad
Angular speed of the flywheel after it has turned through 120 degrees = 3
32 = 12 + 22
32 = (0)2 + (2)(0.2)(2.0944)
3 = 0.9153 rad/s
Radial acceleration of a point at the rim after the flywheel has turned through 120 degrees = a2r
a2r = 32R
a2r = (0.9153)2(0.3)
a2r = 0.251 m/s2
a) Magnitude of the resultant acceleration of a point on the rim after it has turned through 60 degrees = 0.139 m/s2
b) Magnitude of the radial acceleration of a point on the rim after it has turned through 120 degrees = 0.251 m/s2
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