A flywheel with radius of 0.300 m starts from rest and accelerates with a constant angular acceleration of 0.400 rad/s2.For a po
1 answer:
Answer:
Explanation:
Given that,
The radius of a flywheel, r = 0.3 m
Angular acceleration of a flywheel,
We need to find the magnitude of the tangential acceleration after 2.00 s of acceleration.
The relation between the tangential and angular acceleration is given by :
So, the required magnitude of tangential acceleration is .
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(1) The position around equilibrium of an object in simple harmonic motion is described by
where
A is the amplitude of the motion
is the angular frequency.
The velocity is the derivative of the position:
where
is the maximum velocity of the object.
The acceleration is the derivative of the velocity:
where
is the maximum acceleration of the object.
We know from the problem both maximum velocity and maximum acceleration:
From the first equation, we get
(1)
and if we substitute this into the second equation, we find the angular fequency
while the amplitude is (using (1)):
(b) We found in the previous step that the angular frequency of the motion is
But the angular frequency is related to the period by
and so, the period is
where
A is the amplitude of the motion
The velocity is the derivative of the position:
where
The acceleration is the derivative of the velocity:
where
We know from the problem both maximum velocity and maximum acceleration:
From the first equation, we get
and if we substitute this into the second equation, we find the angular fequency
while the amplitude is (using (1)):
(b) We found in the previous step that the angular frequency of the motion is
But the angular frequency is related to the period by
and so, the period is