A disk initially at rest is given an angular
acceleration of 12rad/s. What is its frequency
after 10 seconds?
To find the frequency of the disk after 10 seconds, we need to find the angular velocity first.
Using the formula for angular acceleration:
ω = ω₀ + αt
where ω is the angular velocity, ω₀ is the initial angular velocity (which is 0 since the disk is initially at rest), α is the angular acceleration, and t is the time.
Plugging in the values:
ω = 0 + 12rad/s² * 10s
= 120rad/s
The frequency, f, is given by:
f = ω / (2π)
Plugging in ω:
f = 120rad/s / (2π)
≈ 19.1Hz
Therefore, the frequency of the disk after 10 seconds is approximately 19.1Hz.
To find the frequency of the disk after 10 seconds, we need to first calculate the final angular velocity, and then convert it into frequency.
Given:
Initial angular velocity (ω0) = 0 rad/s (initially at rest)
Angular acceleration (α) = 12 rad/s^2
Time (t) = 10 s
We can use the following formula to find the final angular velocity:
ω = ω0 + αt
Substituting the given values,
ω = 0 + (12 rad/s^2) * 10 s
= 120 rad/s
To convert the final angular velocity into frequency, we can use the formula:
Frequency (f) = ω / (2π)
Substituting the value of ω:
f = 120 rad/s / (2π)
= 120 / (2π) Hz
Therefore, the frequency of the disk after 10 seconds is approximately:
f ≈ 19.1 Hz