Question

A disk with diameter of 60 cm speeds up from 20 rad/s to 40 rad/s in 5 seconds. (a) how many revolutions will the disk go through during that time period?

Answer 1

During the 5-second interval, the disk with a diameter of 60 cm that speeds up from 20 rad/s to 40 rad/s goes through approximately 23.87 revolutions.

Step-by-step explanation:

A student has asked how many revolutions a disk will go through if it speeds up from 20 rad/s to 40 rad/s in 5 seconds with a diameter of 60 cm. To determine the number of revolutions, we first need to calculate the angular displacement using the angular motion formula θ = ωit + ½αt2, where θ is the angular displacement, ωi is the initial angular velocity, α is the angular acceleration, and t is the time.

First, we calculate the angular acceleration ( α ) using the formula α = (ωf - ωi)/t. The initial angular velocity (ωi) is 20 rad/s, the final angular velocity (ωf) is 40 rad/s, and the time (t) is 5 seconds. Then α = (40 rad/s - 20 rad/s) / 5 s = 4 rad/s2.

Next, we calculate the angular displacement (θ), θ = (20 rad/s)(5 s) + ½(4 rad/s2)(5 s)2 = 100 rad + 50 rad = 150 rad.

Now, we convert the angular displacement from radians to revolutions knowing that 1 revolution is 2π radians, so the number of revolutions (n) is n = θ / (2π) = 150 / (2π) ≈ 23.87 revolutions.

Therefore, the disk goes through approximately 23.87 revolutions during the 5-second interval.