Consider the rotational motion of two compact discs (CD). Disc A undergoes a rotation of 540 degrees in 1.50 secs, and disc B undergoes a rotation of π radians in 3.00 secs.
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Consider the rotational motion of two compact discs (CD). Disc A undergoes a rotation of 540 degrees in 1.50 secs, and disc B undergoes a rotation of π radians in 3.00 secs.
a) Angular speed (A) = 4π radians/sec
Angular speed (B) = 60 degrees/sec
b) Angular speed (A) = 2π radians/sec
Angular speed (B) = 60 degrees/sec
c) Angular speed (A) = 6π radians/sec
Angular speed (B) = 360 degrees/sec
d) Angular speed (A) = 3π radians/sec
Angular speed (B) = 180 degrees/sec
To analyze the rotational motion of the two compact discs (CDs), we need to understand the basic concepts of rotational motion.
First, let's convert the given values into radians, as radians are the preferred unit for measuring rotational angles.
1. For disc A:
Given rotation = 540 degrees
To convert degrees to radians, we use the conversion factor: 1 radian = π/180 degrees
Thus, rotation of disc A in radians = (540 degrees) * (π/180 degrees) = 3π radians
2. For disc B:
Given rotation = π radians
Now that we have the rotational angles in radians, we can proceed to analyze the motion of the discs.
The angular displacement (θ) of an object undergoing rotational motion is given by the formula:
θ = ω * t
where:
θ is the angular displacement in radians,
ω is the angular velocity in radians per second, and
t is the time in seconds.
For disc A:
Given θ = 3π radians and t = 1.50 seconds,
we can rearrange the formula to find ω:
ω = θ / t = (3π radians) / (1.50 seconds) = 2π radians/second
So, the angular velocity of disc A is 2π radians/second.
For disc B:
Given θ = π radians and t = 3.00 seconds,
we can also find the angular velocity ω using the same formula:
ω = θ / t = (π radians) / (3.00 seconds) = π/3 radians/second
Thus, the angular velocity of disc B is π/3 radians/second.
In summary:
Disc A's angular velocity = 2π radians/second
Disc B's angular velocity = π/3 radians/second
Understanding the angular velocity of objects undergoing rotational motion is crucial for analyzing their behavior.