Question

The angular velocity of a rotating turntable is given in rad/s by ω(t) = 4.5 + 0.64t – 2.1t^2. What is its average angular acceleration between t = 1.0 s and t = 3.0 s?

Answer 1

The average angular acceleration of the rotating turntable between t = 1.0 s and t = 3.0 s is calculated by finding the change in angular velocity over the change in time, yielding an average angular acceleration of -7.76 rad/s².

Step-by-step explanation:

To determine the average angular acceleration of the rotating turntable between t = 1.0 s and t = 3.0 s, we need to find the change in angular velocity over the change in time. The angular velocity function is given by ω(t) = 4.5 + 0.64t – 2.1t2. To find the angular velocities at the specific times, we evaluate:

• ω(1.0) = 4.5 + 0.64(1.0) – 2.1(1.0)2
• ω(3.0) = 4.5 + 0.64(3.0) – 2.1(3.0)2

Let's calculate:

• ω(1.0) = 4.5 + 0.64 - 2.1 = 3.04 rad/s
• ω(3.0) = 4.5 + 1.92 - 18.9 = -12.48 rad/s

The change in angular velocity (Δω) is ω(3.0) - ω(1.0):

• Δω = -12.48 rad/s - 3.04 rad/s = -15.52 rad/s

The change in time (Δt) is 3.0 s - 1.0 s = 2.0 s.

Therefore, the average angular acceleration (αavg) is:

• αavg = Δω / Δt = -15.52 rad/s / 2.0 s = -7.76 rad/s2