Question

ACD player disk starts from rest, and has a positive angular acceleration (it begins to spin quicker and quicker in the counter clockwise direction) of 3.5 radians per second squared, for 43 seconds. Then, it stays at that angular velocity for 300 radians. Finally, after you are done listening to the song, the CD begins to slow to a rest, which takes 44 seconds. Please round all answers to the nearest whole number. 1. How many radians did the CD spin total?

Answer 1

To find the total angular displacement of the CD, calculate the angular displacement for each phase (acceleration, constant velocity, deceleration) and sum them: 3234.25 + 300 + 3234.25 = 6768.5 radians, rounded to 6834 radians.

The question involves calculating the total angular displacement of a CD player disk with a given angular acceleration, followed by a phase of constant angular velocity, and finally a deceleration back to rest. To calculate the angular displacement during the acceleration phase, we can use the equation θ = 0.5•α•t², where α is the angular acceleration and t is the time. So, for the first phase with α = 3.5 rad/s² and t = 43 s, θ = 0.5•(3.5 rad/s²)•(43 s)² = 3234.25 radians. For the phase of constant angular velocity, the CD spins for an additional 300 radians. The deceleration phase also has an angular displacement using the same formula as acceleration because angular acceleration is symmetrical for stopping and starting when the rates are the same and time period is the same.

The CD player disk spins for a total of 6834 radians approximated to the nearest whole number when combining the angular displacements of all three phases.

The method to find the total angular displacement is to calculate each phase of motion separately and then sum them together. In cases where angular acceleration and deceleration occur over the same time period and rate, the displacements for these periods will be the same.