Question

A figure skater begins spinning counterclockwise at an angular speed of 3.2 π rad/s. During a 4.2 s interval, she slowly pulls her arms

inward and finally spins at 8.8 π rad/s.
What is her average angular acceleration
during this time interval?
Answer in units of rad/s^2

Answer 1

To find the average angular acceleration, subtract the initial angular speed from the final angular speed and divide by the time interval. The calculation results in an average angular acceleration of 4.21 rad/s².

Step-by-step explanation:

The student's question involves determining the average angular acceleration of a figure skater who increases her spin rate from an initial angular speed to a final angular speed over a given time interval. Since angular acceleration is the rate of change of angular speed, we can calculate it using the formula:

average angular acceleration (α) = (ω_final - ω_initial) / t

Where:

• ω_final is the final angular speed
• ω_initial is the initial angular speed
• t is the time interval

Given:

• ω_initial = 3.2 π rad/s
• ω_final = 8.8 π rad/s
• t = 4.2 s

The calculation is as follows:

average angular acceleration (α) = (8.8 π - 3.2 π) rad/s / 4.2 s

= 5.6 π rad/s / 4.2 s
= 4.21 rad/s²

Answer 2

4.2 rad/s²

Step-by-step explanation:

Given:

ω₀ = 3.2π rad/s

ω = 8.8π rad/s

t = 4.2 s

Find: α

ω = αt + ω₀

8.8π rad/s = α (4.2 s) + 3.2π rad/s

α = 4.2 rad/s²