A flywheel with a radius of 0.310m{\ m m} starts from rest and accelerates with
ID: 1289290 • Letter: A
Question
A flywheel with a radius of 0.310m{ m m} starts from rest and accelerates with a constant angular acceleration of 0.630rad/s2{ m rad/s^{2}} .
B.
A flywheel with a radius of 0.310m{ m m} starts from rest and accelerates with a constant angular acceleration of 0.630rad/s2{ m rad/s^{2}} . A. Compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim after it has turned through 60.0? B. B.Compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim after it has turned through 120?Explanation / Answer
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A flywheel with a radius of 0.310 m starts from rest and accelerates with a constant angular acceleration of 0.660 rad/s2 . Compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim after it has turned through 60.0 degrees.Compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim after it has turned through 120 degrees.
Answer
The formulae for components of acceleration of a particle moving in a curve with polar co-ordinates (r, t) are:
Normal: r''- r(t')^2
Tangential: rt''+ 2r't'
For circular motion r' and r'' are zero, yielding:
Normal: - r(t')^2
Tangential: rt''
For the flywheel, the normal acceleration of a particle on the rim at the start is:
0, as t' is initially 0.
The tangential acceleration is:
0.310 * 0.660
= 0.2046m/s^2.
The resultant acceleration is the same as the tangential.
When the flywheel has rotated through pi/3 (= 60 deg):
(t')^2 = 2 * 0.660 * pi/3
t = 1.175 rad/s.
The normal acceleration is:
- 0.310 * 2 * 0.66 * pi / 3
= - 0.4285 m/s^2.
The tangential acceleration is still 0.2046 m/s^2, as it is constant.
The resultant accleration is of magnitude:
sqrt(0.4285^2 + 0.2046^2)
= 0.4748 m/s^2.
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