A 36 cm diameter wheel accelerates uniformly about its center from 150 rpm to 360 rpm in 3.6 s. Determine the radial component of the linear acceleration of a point on the edge of the wheel 1.1 s after it has started accelerating.

To determine the radial component of the linear acceleration of a point on the edge of the wheel 1.1 seconds after it has started accelerating, we can use the formula for linear acceleration in terms of rotational motion:

a = α * r

Where:
a is the linear acceleration,
α is the angular acceleration, and
r is the radius.

First, let's find the angular acceleration:

We're given the initial and final angular velocities and the time it took to reach the final velocity. We can use the formula for angular acceleration:

α = (ωf - ωi) / t

where:
α is the angular acceleration,
ωf is the final angular velocity (in radians per second),
ωi is the initial angular velocity (in radians per second), and
t is the time taken (in seconds).

To convert rpm to radians per second, use the conversion factor:
1 revolution = 2π radians

Given:
ωi = 150 rpm
ωf = 360 rpm
t = 3.6 s

Converting ωi and ωf to radians per second:
ωi = 150 rpm * 2π/60 s = 15.71 rad/s
ωf = 360 rpm * 2π/60 s = 37.70 rad/s

Hence, the angular acceleration (α) is:
α = (37.70 rad/s - 15.71 rad/s) / 3.6 s = 5.97 rad/s²

Next, we need to determine the radius of the wheel:

The diameter of the wheel is given as 36 cm, and the radius is half the diameter, so:
r = 36 cm / 2 = 18 cm = 0.18 m

Now we can calculate the linear acceleration at 1.1 seconds:

Using the formula a = α * r, we can substitute the values:
a = 5.97 rad/s² * 0.18 m = 1.0746 m/s²

Therefore, the radial component of the linear acceleration of a point on the edge of the wheel 1.1 seconds after it has started accelerating is approximately 1.07 m/s².