A figure skater begins spinning counterclockwise at an angular speed of 4.2 π rad/s. During a 4.5 s interval, she slowly pulls her arms
inward and finally spins at 7.7 π rad/s.
What is her average angular acceleration
during this time interval?
Answer in units of rad/s^2
acceleration = change in speed / change in time
= (7.7 - 4.2) pi / 4.5 rad/s^2
V = Vo + a*T.
7.7pi = 4.2pi + a*4.5,
4.5a = 7.7pi-4.2pi = 3.5pi,
a = 2.44 rad/s^2.
To find the average angular acceleration, we need to calculate the change in angular speed and divide it by the change in time.
The initial angular speed is given as 4.2π rad/s, and the final angular speed is 7.7π rad/s. The time interval is 4.5 s.
Change in angular speed = Final angular speed - Initial angular speed
= 7.7π rad/s - 4.2π rad/s
= 3.5π rad/s
Average angular acceleration = Change in angular speed / Time interval
= (3.5π rad/s) / (4.5 s)
≈ 2.45 rad/s^2
Therefore, the average angular acceleration during this time interval is approximately 2.45 rad/s^2.
To find the average angular acceleration, we need to use the formula for angular acceleration:
angular acceleration = (final angular velocity - initial angular velocity) / time
In this case, the initial angular velocity is 4.2π rad/s, the final angular velocity is 7.7π rad/s, and the time interval is 4.5 s.
Plugging these values into the formula, we get:
angular acceleration = (7.7π rad/s - 4.2π rad/s) / 4.5 s
Simplifying the expression inside the parentheses, we have:
angular acceleration = 3.5π rad/s / 4.5 s
Dividing 3.5π rad/s by 4.5 s, we get:
angular acceleration ≈ 0.7778π rad/s²
Rounding to the nearest thousandth, the average angular acceleration during this time interval is approximately 0.778π rad/s².