a) The initial angular speed is 209.3 m/s
b) The angular acceleration is
c) The angular speed after 40 s is 139.7 rad/s
d) The wheel makes 1501 revolutions
Explanation:
a)
The initial angular speed of the wheel is
which means 2000 revolutions per minute.
We have to convert it into rad/s. Keeping in mind that:
We find:
b)
To find the angular acceleration, we have to convert the final angular speed also from rev/min to rad/s.
Using the same procedure used in part a),
Now we can find the angular acceleration, given by
where
is the initial angular speed
is the final angular speed
t = 60 s is the time interval
Substituting,
c)
To find the angular speed 40 seconds after the initial moment, we use the equivalent of the suvat equations for circular motion:
where we have
And substituting t = 40 s, we find
d)
The angular displacement of the wheel in a certain time interval t is given by
where
And substituting t = 60 s, we find:
So, the wheel turns 9426 radians in the 60 seconds of slowing down. Converting this value into revolutions,
Learn more about circular motion:
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