An ice skater rotating around a vertical axis increases in angular velocityfrom 450degrees/s to 610degrees/s in 2.3 seconds. Find the angular acceleration
acceleration is the rate of change of velocity, so
a = (610-450)/(2.3
= 69.57 degrees/s^2
Well, that ice skater certainly knows how to spin it to win it! Let's calculate the angular acceleration using the information provided.
We know that angular acceleration (α) is defined as the change in angular velocity (ω) divided by the change in time (t):
α = (ωf - ωi) / t
Substituting the given values, we have:
α = (610°/s - 450°/s) / 2.3s
Now, let's plug in the numbers and calculate this circus act of an angular acceleration:
α = (160°/s) / 2.3s
α ≈ 69.57°/s^2
So, the angular acceleration of the ice skater is approximately 69.57 degrees per second squared. That's one spin-tastic acceleration!
To find the angular acceleration, we can use the equation:
Angular acceleration (α) = Change in angular velocity (Δω) / Time (Δt)
Given:
Initial angular velocity (ωi) = 450 degrees/s
Final angular velocity (ωf) = 610 degrees/s
Time (Δt) = 2.3 seconds
First, we need to find the change in angular velocity (Δω):
Δω = ωf - ωi
= 610 degrees/s - 450 degrees/s
= 160 degrees/s
Now, we can substitute the values into the formula for angular acceleration:
α = Δω / Δt
= 160 degrees/s / 2.3 s
≈ 69.57 degrees/s^2
Therefore, the angular acceleration of the ice skater is approximately 69.57 degrees/s^2.
To find the angular acceleration, we can use the formula:
Angular acceleration (α) = (Change in angular velocity) / (Change in time)
Given:
Initial angular velocity (ω₀) = 450 degrees/s
Final angular velocity (ω) = 610 degrees/s
Change in time (Δt) = 2.3 seconds
Substituting these values into the formula:
α = (ω - ω₀) / Δt
α = (610 degrees/s - 450 degrees/s) / 2.3 seconds
Simplifying:
α = 160 degrees/s / 2.3 seconds
α ≈ 69.57 degrees/s²
Therefore, the angular acceleration is approximately 69.57 degrees/s².