Final answer:
The angular acceleration of an electric drill that reaches 1800 rpm in 2.5 seconds is calculated by first converting rpm to rad/s and then using the formula for angular acceleration (α = (ω - ω_0) / δt), which results in 75.3984 rad/s².
Step-by-step explanation:
To calculate the angular acceleration of an electric drill that requires 2.5 seconds to reach a speed of 1800 rpm, first, we need to convert the rpm to radians per second (rad/s). Since 1 revolution is 2π radians and there are 60 seconds in a minute, we get:
ω = 1800 rpm × (2π rad/rev) × (1 min/60 s) = 1800 × 2π × 1/60 = 188.496 rad/s
The drill starts from rest, so its initial angular speed (ω0) is 0. The angular acceleration (α) can then be calculated using the formula:
α = (ω - ω0) / δt
Substituting the values we have:
α = (188.496 rad/s) / 2.5 s = 75.3984 rad/s²
Therefore, the angular acceleration of the drill is 75.3984 rad/s².