a) The angular velocity is 0.004 rad/s
b) The linear velocity is
c) The period of motion is 235 s
Explanation:
a)
The angular velocity of an object in circular motion is the rate of change of the angular position of the object. It can be calculated as follows:
where
s is the arc of length covered by the object
t is the time elapsed
For the stone moving in the horizontal circle in the problem, we have
s = 4 cm = 0.04 m is the length of the arc covered
t = 10 s is the time elapsed
Substituting, we find the angular velocity:
b)
In a circular motion, the linear velocity is related to the angular velocity by the equation
where
is the linear velocity
is the angular velocity
r is the radius of the circle
For the stone in this problem, we have:
(angular velocity, calculated in part a)
r = 15 cm = 0.15 m (radius of the circle)
Substituting, we find
c)
In a circular motion, the period is the time taken for the object to complete exactly one revolution.
The circle in this problem has a radius of
r = 0.15 m
So, the circumference is
We know that the stone covers an arc length of s = 0.04 m in 10 s, therefore we can use the following proportion to find the time taken for the stone to cover one circumference (and this time is the period of the motion):
Learn more about circular motion:
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