Question

After 4.30 s of constant angular acceleration, a dentist's drill turns at a rate of 2.05 ✕ 10⁴ rev/min. What is the angular acceleration of the drill?

Answer 1

To determine the angular acceleration of the dentist's drill, convert its final angular velocity to rad/s and apply the formula for constant angular acceleration. By applying this calculation, the angular acceleration can be determined over the 4.30 second time interval.

Step-by-step explanation:

The question asks for the angular acceleration of a dentist's drill. Given that the drill reaches an angular velocity of 2.05 × 10⁴ rev/min after 4.30 seconds of constant angular acceleration, we need to convert rev/min to rad/s and then use the formula for angular acceleration, α = (ω - ω₀) / t, where α is angular acceleration, ω is final angular velocity, ω₀ is initial angular velocity (which is zero in this case, since the drill starts from rest), and t is time.

First, convert the angular velocity from rev/min to rad/s:

• 2.05 × 10⁴ rev/min × (1 min / 60 s) × (2π rad / 1 rev) = 2.05 × 10⁴ × × 2π / 60 rad/s

Now, calculate the angular acceleration:

• α = (ω - ω₀) / t = (2.05 × 10⁴ × 2π / 60) / 4.30 rad/s²