A flywheel with a diameter of 1 m is initially at rest. Its angular acceleration versus time is graphed in the figure.
(a) What is the angular separation between the initial position of a fixed point on the rim of the flywheel and the point's position 8 s after the wheel starts rotating? (Be sure to give angular separation rather than total angular displacement.)
(b) The point starts its motion at θ = 0. Calculate the linear position 8 s after the wheel starts rotating. (Let the initial position of the point be 0.5 .)
m
Calculate the linear velocity vector 8 s after the wheel starts rotating. (Enter the magnitude.)
Calculate the tangential acceleration vector after the wheel starts rotating. (Enter the magnitude.)
To answer the questions, we need to use the given information about the angular acceleration versus time graph and the diameter of the flywheel.
(a) To find the angular separation between the initial position and the position after 8 s, we need to integrate the angular acceleration with respect to time to find the angular velocity, and then integrate the angular velocity with respect to time to find the angular displacement.
Given that the graph of angular acceleration versus time is not provided, we cannot directly find the angular velocity and angular displacement. You would need to provide more information or a different graph to solve this part of the question.
(b) To calculate the linear position 8 s after the wheel starts rotating, we can use the formula:
θ = ω_0t + (1/2)αt^2,
where θ is the angular displacement, ω_0 is the initial angular velocity, α is the angular acceleration, and t is the time.
Given that the initial position of the point is 0.5 m, we can solve for θ.
θ = (0.5)(8) + (1/2)(α)(8)^2.
Please note that the value of α from the graph is needed to complete this calculation.
To calculate the linear velocity vector 8 s after the wheel starts rotating, we can use the formula:
v = ωR,
where v is the linear velocity, ω is the angular velocity, and R is the radius of the flywheel.
The radius of the flywheel can be found by dividing the diameter by 2 (R = 1 m/2 = 0.5 m).
Given that the angular velocity is obtained by integrating the angular acceleration, we need the graph of angular acceleration versus time to calculate the angular velocity.
Similarly, to calculate the tangential acceleration vector after the wheel starts rotating, we need the angular acceleration at that time from the graph.
Please provide the graph or more information so that we can proceed with the calculations.