Calculating Angular Acceleration of a Washer's Tub

[smd1991]

1. The tub of a washer goes into its spin-dry cycle, starting from rest and reaching an angular speed of 2.2 revolutions/s in 8.4 seconds. at this point the person doing the laundry opens the lid, and a safety switch turns off the washer, the tub slows to rest in 9.5 seconds.
through how many revolutions does the tub turn? assume constant angular acceleration while it is starting and stopping. answer in units of revolution.




i don't even know where to start really, besides finding the angular acceleration

 

[mezarashi]

Do you have the kinematics equations for angular displacement? The process is exactly the same as how you would do it linearly.

1. washing machine starts from rest and goes to a final velocity of 2.2 in 8.4s.
2. washing machine then goes from 2.2 to rest in 9.5s.
3. what is the total distance traveled by washing machine (freaky huh, washing machines that can run out of the house).

 

[ogb p]

. we can use the formula ωf = ωi + αt to find the angular acceleration. ωf is the final angular speed (2.2 revolutions/s), ωi is the initial angular speed (0 revolutions/s), α is the angular acceleration, and t is the time (8.4 seconds). rearranging the formula, we get α = (ωf - ωi)/t. plugging in the values, we get α = (2.2 - 0)/8.4 = 0.262 revolutions/s^2.

now, using the formula θ = ωi*t + 0.5*α*t^2, we can find the number of revolutions the tub turns while accelerating. θ is the total angle turned (unknown), ωi is the initial angular speed (0 revolutions/s), t is the time (8.4 seconds), and α is the angular acceleration (0.262 revolutions/s^2). rearranging the formula, we get θ = 0.5*α*t^2. plugging in the values, we get θ = 0.5*0.262*8.4^2 = 9.856 revolutions.

since the tub reaches an angular speed of 2.2 revolutions/s, it will turn an additional 2.2 revolutions in the 9.5 seconds it takes to slow down and come to rest. therefore, the total number of revolutions the tub turns is 9.856 + 2.2 = 12.056 revolutions.

assuming constant angular acceleration while starting and stopping, the tub turns 12.056 revolutions in total.