Question

The angle through which a rotating wheel has turned in time t is given by θ = a t− b t2+ c t4, where θ is in radians and t in seconds.

Just need help answering

What is the average angular velocity between t = 2.0 s and t =3.1 s ?

Answer 1

To compute the average angular velocity, calculate the angular positions at t = 2.0 s and t = 3.1 s using the given formula, then use these positions to find the change in angle over the change in time between these time points.

Step-by-step explanation:

To find the average angular velocity between two points in time given the equation θ = a t - b t2 + c t4, where θ is in radians and t is time in seconds, we can use the initial and final angular positions at the given times to calculate it.

First, find the angular position at t = 2.0 s (θinitial) and t = 3.1 s (θfinal) by plugging the times into the given equation. Next, the average angular velocity (ωavg) between t = 2.0 s and t = 3.1 s is given by:

ωavg = ∆θ / ∆t = (θfinal - θinitial) / (tfinal - tinitial)

Substitute the calculated values of θfinal and θinitial and compute the difference in times (3.1 s - 2.0 s) to get the average angular velocity.