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.
see other post.
To find the radial component of the linear acceleration of a point on the edge of the wheel 1.0 second after it has started accelerating, we can use the formula for linear acceleration:
a = (vf - vi) / t
where a is the linear acceleration, vf is the final velocity, vi is the initial velocity, and t is the time.
In this case, the wheel's diameter is given as 44 m, which means its radius is half of the diameter, or 22 m.
The initial velocity, vi, can be calculated from the given information. The initial velocity is 110 rpm, which needs to be converted to m/s. To do this, we can use the formula:
v = ω * r
where v is the linear velocity, ω is the angular velocity (in radians per second), and r is the radius.
First, we need to convert rpm to radians per second. There are 2π radians in one revolution, and 60 seconds in one minute. Therefore, we can calculate the initial velocity as follows:
vi = (110 rpm) * (2π radians/1 rev) * (1 min/60 s) * (22 m)
= (110 rpm) * (2π radians/1 rev) * (1 min/60 s) * (22 m)
= (110 * 2π * 22) / 60 m/s
Similarly, the final velocity, vf, can be calculated using the same steps but with a velocity of 320 rpm.
vf = (320 rpm) * (2π radians/1 rev) * (1 min/60 s) * (22 m)
= (320 * 2π * 22) / 60 m/s
Now, we can calculate the linear acceleration a using the formula mentioned earlier:
a = (vf - vi) / t
= [(320 * 2π * 22) / 60 - (110 * 2π * 22) / 60] / 3.9 m/s^2
Simplifying the above expression will give you the value of the radial component of the linear acceleration at 1.0 second after the wheel starts accelerating.