Some radar systems detect the size and shape of objects such as aircraft and geological terrain. What is the frequency of such a
1 answer:
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A) Angular speed: 0.42 rev/s
B) Frequency: 0.42 Hz
C) Tangential speed: 26.4 cm/s
D) Distance travelled: 528 cm
Explanation:
A)
In this problem, the ladybug is rotating together with the record.
The angular velocity of the ladybug, which is defined as the rate of change of the angular position of the ladybug, in this problem is
where here it is measured in revolutions per minute.
Keeping in mind that
1 minute = 60 seconds
We can rewrite the angular speed in revolutions per second:
B)
The relationship between angular speed and frequency of revolution for a rotational motion is given by the equation
(1)
where
is the angular speed
f is the frequency of revolution
For the ladybug in this problem,
Keeping in mind that , the angular speed can be rewritten as
And re-arranginf eq.(1), we can find the frequency:
And the frequency is the number of complete revolutions made per second.
C)
For an object in circular motion, the tangential speed is related to the angular speed by the equation
where
is the angular speed
v is the tangential speed
r is the distance of the object from the axis of rotation
For the ladybug here,
is the angular speed
r = 10 cm = 0.10 m is the distance from the center of the record
So, its tangential speed is
D)
The tangential speed of the ladybug in this motion is constant (because the angular speed is also constant), so we can find the distance travelled using the equation for uniform motion:
where
v is the tangential speed
t is the time elapsed
Here we have:
v = 26.4 cm/s (tangential speed)
t = 20 s
Therefoe, the distance covered by the ladybug is
Learn more about circular motion:
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A = distance traveled by steve in north direction by train = 30 miles
B = distance traveled by steve in east direction by train = 25 miles
R = resultant displacement of the steve relative to starting position
using pythagorean theorem
R = √(A² + B²)
inserting the values
R = √(30² + 25²)
R = 39.05 miles
direction : tan⁻¹(B/A) = tan⁻¹(25/30) = 39.8 deg east of north
