The average angular velocity is defined as which expression?

The average angular velocity is defined as which expression?

• A. omega = theta / t
• B. omega = delta theta / delta t
• C. omega = delta s / delta t
• D. omega = delta theta / delta t^2

Answer: (B)

The main idea is that how fast something is rotating on average over a time interval is given by how much angle it sweeps divided by how long that sweep takes. The average angular velocity is the change in angular displacement Δθ divided by the change in time Δt, so ω_avg = Δθ/Δt. Here θ (or Δθ) is measured in radians, so the units come out as rad/s, just like linear speed is distance over time. Why this is the right form: it directly mirrors the linear case where average speed is displacement over time. If you rotate from one angle to another in a certain time, you’ve covered that angular displacement in that time, which is exactly what the ratio Δθ/Δt captures. For instantaneous angular velocity you’d take the limit as Δt goes to zero, yielding ω = dθ/dt. The other expressions don’t fit: using θ without a Δ implies the total angle divided by total time but omits the starting point and is ambiguous; using Δs/Δt gives linear speed, not angular speed; dividing by (Δt) squared would have the wrong units and dimension.

The main idea is that how fast something is rotating on average over a time interval is given by how much angle it sweeps divided by how long that sweep takes. The average angular velocity is the change in angular displacement Δθ divided by the change in time Δt, so ω_avg = Δθ/Δt. Here θ (or Δθ) is measured in radians, so the units come out as rad/s, just like linear speed is distance over time.

Why this is the right form: it directly mirrors the linear case where average speed is displacement over time. If you rotate from one angle to another in a certain time, you’ve covered that angular displacement in that time, which is exactly what the ratio Δθ/Δt captures. For instantaneous angular velocity you’d take the limit as Δt goes to zero, yielding ω = dθ/dt.

The other expressions don’t fit: using θ without a Δ implies the total angle divided by total time but omits the starting point and is ambiguous; using Δs/Δt gives linear speed, not angular speed; dividing by (Δt) squared would have the wrong units and dimension.