Final answer:
To find the number of additional revolutions the wheel will make, we must first determine the angular acceleration using the given data that the wheel completes 8.0 revolutions in the first 2.5 seconds. Then, apply kinematic equations for rotational motion to calculate the further number of revolutions over the next 14.0 seconds.
Step-by-step explanation:
The student's question involves calculating the number of additional revolutions made by a wheel that is subject to uniform angular acceleration. Maths within the field of physics specifically related to kinematics of rotational motion is required to solve the problem.
The scenario is one where a wheel is starting from rest and we are given that it completes 8.0 revolutions in the first 2.5 seconds. The key is to apply the kinematic equations for rotational motion to find out the angular acceleration and then use it to calculate the number of further revolutions over the next 14.0 seconds.
The formula to find the total angle θ in radians that the wheel has turned is θ = ω0t + ½ αt2, where ω0 is the initial angular velocity, α is the angular acceleration, and t is the time. Since the wheel starts from rest, ω0 = 0. To find the angular acceleration α, we can first convert revolutions to radians (1 revolution = 2π radians) and then rearrange the equation to α = (2θ)/t2.
After finding α, we could use the angular displacement formula again to calculate how many additional revolutions the wheel will complete in the next 14.0 seconds.