A 44 m diameter wheel accelerates uniformly about its center from 110 rpm to 320 rpm in 3.9 s.
Determine the radial component of the linear acceleration of a point on the edge of the wheel 1.0 s after it has started accelerating.
To determine the radial component of the linear acceleration of a point on the edge of the wheel 1.0 s after it has started accelerating, we can use the formula for linear acceleration:
Linear acceleration (a) = change in velocity (Δv) / time interval (Δt)
First, let's calculate the change in velocity:
Change in velocity (Δv) = final velocity (v_f) - initial velocity (v_i)
Given:
Initial velocity (v_i) = 110 rpm
Final velocity (v_f) = 320 rpm
Convert the initial and final velocities from rpm to m/s:
v_i = (110 rpm) * (π rad/30 s) * (44 m/2) = 254.46 m/s
v_f = (320 rpm) * (π rad/30 s) * (44 m/2) = 727.74 m/s
Therefore, Δv = 727.74 m/s - 254.46 m/s = 473.28 m/s
Next, let's calculate the time interval:
Δt = 3.9 s - 1.0 s = 2.9 s
Now, we can calculate the linear acceleration:
a = (Δv) / (Δt) = 473.28 m/s / 2.9 s = 163.18 m/s^2
Therefore, the radial component of the linear acceleration of a point on the edge of the wheel 1.0 s after it has started accelerating is 163.18 m/s^2.