Final answer:
The radial component of the linear acceleration of a point on the edge of the wheel 2.0s after it started accelerating is 135.84 m/s².
Step-by-step explanation:
To determine the radial component of the linear acceleration of a point on the edge of the wheel, we need to calculate the angular acceleration first. Given the initial angular velocity (ωinitial) of 130rpm and the final angular velocity (ωfinal) of 290rpm over a time (Δt) of 4.8s, we can use the formula for angular acceleration (α), which is α = (ωfinal - ωinitial) / Δt.
Converting the angular velocities from rpm to rad/s:
- ωinitial = 130rpm × (2π rad/1 rev) × (1 min/60s) = 13.61 rad/s
- ωfinal = 290rpm × (2π rad/1 rev) × (1 min/60s) = 30.39 rad/s
Next, we calculate the angular acceleration:
- α = (30.39 rad/s - 13.61 rad/s) / 4.8s = 3.50 rad/s²
At 2.0s after it has started accelerating, the radial (centripetal) acceleration (ar) of a point on the edge of the wheel can be found using the formula ar = rα², where r is the radius of the wheel. The radius (r) can be found by halving the diameter (D = 64 cm), giving us r = 32 cm = 0.32 m.
First, we find the angular velocity at t = 2.0s:
- ω = ωinitial + αt = 13.61 rad/s + 3.50 rad/s² × 2.0s = 20.61 rad/s.
Finally, we calculate the radial acceleration at t = 2.0s:
- ar = rα² = 0.32 m × (20.61 rad/s)² = 135.84 m/s²