a) The angular speed is 136.1 rad/s
b) The tangential speed is 3.97 m/s
c) The radial acceleration is
d) The total distance covered by a point on the rim in 1.94 s is 21.3 m
Explanation:
a)
We want to determine the angular speed of the disk, which is given by the ratio between the angular displacement and the time taken:
where is the angular displacement and t the time taken.
In this problem, we are already given the angular speed, which is
We need to convert it into rad/sec. Keeping in mind that
we have
b)
The tangential speed of a point on the disk is given by
where
is the angular speed
r is the distance of the point from the axis of rotation
In this problem, we have
r = 2.92 cm = 0.0292 m
Substituting,
c)
The radial acceleration (also called centripetal acceleration) of a point on the disk is given by
where
is the angular speed
r is the distance of the point from the axis of rotation
Here we have:
r = 8.06 cm = 0.0806 m is the distance of a point on the rim from the axis
Substituting,
d)
The total distance covered by a point on the rim in a certain time t is given by
where
v is the tangential speed of a point on the rim
t is the time
Since the tangential speed can be rewritten as , the previous equation becomes
where we have:
r = 8.06 cm = 0.0806 m
t = 1.94 s
Substituting,
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