A flywheel accelerates from rest to an angular velocity of 10.44rad/s at an angular acceleration of 51.57rad/s^2. The diameter of the flywheel is 1.16m.
At this instant, calculate the resultant linear acceleration, in m/s^2, of a point on the circumference of the flywheel.
ω = 10.44rad/s ,
ε = 51.57rad/s^2
R =D/2.
Normal (centripetal) acceleration
a(n) = ω^2•R.
Tangential acceleration
a(τ) = ε•R.
Resultant linear acceleration
a =sqrt(a(n)^2 + a(τ)^2).
To calculate the resultant linear acceleration of a point on the circumference of the flywheel, we can use the following formula:
Linear Acceleration = Radius x Angular Acceleration
First, let's find the radius of the flywheel. We know that the diameter of the flywheel is 1.16m, so the radius (r) can be calculated by dividing the diameter by 2:
r = diameter / 2 = 1.16m / 2 = 0.58m
Next, we'll substitute the values into the formula:
Linear Acceleration = 0.58m x 51.57rad/s^2
Calculating the result:
Linear Acceleration ≈ 29.9316 m/s^2
Therefore, at this instant, the resultant linear acceleration of a point on the circumference of the flywheel is approximately 29.9316 m/s^2.