Answer:
α = 821 rad/s²
Δθ = 4.21×10³ rad
Explanation:
The drill turns with a constant acceleration, so we can use kinematic equations known as SUVAT equations to solve for the angular acceleration and angular displacement (the angle of rotation). In this case, the equations we will use are:
ω = αt + ω₀
Δθ = ½ (ω + ω₀) t
where
- Δθ is the angular displacement (angle of rotation)
- ω₀ is the initial angular velocity
- ω is the final angular velocity
- α is the angular acceleration
- t is the time
Given:
ω₀ = 0 rad/s
ω = 2.51×10⁴ rev/min × (2π rad/rev) × (1 min / 60 s) = 2.63×10³ rad/s
t = 3.20 s
(a) Use the first equation to find the angular acceleration α.
ω = αt + ω₀
2.63×10³ rad/s = α (3.20 s) + 0 rad/s
α = 821 rad/s²
(b) Use the second equation to find the angular displacement Δθ.
Δθ = ½ (ω + ω₀) t
Δθ = ½ (2.63×10³ rad/s + 0 rad/s) (3.20 s)
Δθ = 4.21×10³ rad
