A figure skater begins spinning counterclockwise at an angular speed of 4.6π rad/s. During a 4.6s interval, she slowly pulls her arms inward and finally spins at 7.6π rad/s.
What is her average angular acceleration
during this time interval?
Answer in units of rad/s^2.
To calculate the average angular acceleration, we need to use the formula:
Average angular acceleration = (Final angular speed - Initial angular speed) / Time
Given:
Initial angular speed (ω1) = 4.6π rad/s
Final angular speed (ω2) = 7.6π rad/s
Time (t) = 4.6 s
Substituting these values into the formula, we have:
Average angular acceleration = (7.6π rad/s - 4.6π rad/s) / 4.6 s
= (3π rad/s) / 4.6 s
= 0.652π rad/s^2
Therefore, the average angular acceleration during the time interval is approximately 0.652π rad/s^2.
To find the average angular acceleration, we can use the formula:
Average angular acceleration (α) = (final angular velocity - initial angular velocity) / time
Given:
Initial angular velocity (ωi) = 4.6π rad/s
Final angular velocity (ωf) = 7.6π rad/s
Time (t) = 4.6 s
Substituting the given values into the formula, we get:
Average angular acceleration (α) = (7.6π rad/s - 4.6π rad/s) / 4.6 s
Simplifying the expression:
α = 3π rad/s / 4.6 s
Now dividing the numerator and denominator by 4.6:
α = (3π/4.6) rad/s^2
Thus, the average angular acceleration during this time interval is approximately 0.652π rad/s^2.
ω2 = ω1 +ε•t,
ε = (ω2 - ω1)/t=
=(7.6π -4.6 π)/4.6=2.05 rad/s^2