How Do You Calculate Angular Acceleration of a Salad Spinner?

[Steelers72]

Homework Statement

Dario, a prep cook at an Italian restaurant, spins a salad spinner 20.0 times in 5.00 seconds and then stops spinning it. The salad spinner rotates 6.00 more times before it comes to rest. Assume that the spinner slows down with constant angular acceleration.

What is the angular acceleration of the salad spinner as it slows down? Express your answer numerically in radians per second per second.

2. Homework Equations
ω2f = ω20 + 2α(θ)

The Attempt at a Solution

ω = θ / t
ω = 20 * 2 * π / 5.00
ω = 8π
ω = 25.13272 radians/s

now I can solve for α using a kinematic equation:

ω2f = ω20 + 2α(θ)
02 = 25.132722 + 2 * α * (2 * π * 6.00)
0 = 631.6536 + 75.39816α
75.39816α = -631.6536
α = -8.37757 radians/s2

apparently This answer is wrong...where did I go wrong?

 

[Chestermiller]

Significant figures??

Chet

 

[Steelers72]

Significant figures??

Chet

-8.0 didnt work as well.

 

[Chestermiller]

-8.0 didnt work as well.

-8.38??

Chet

 

[SammyS]

Homework Statement

Dario, a prep cook at an Italian restaurant, spins a salad spinner 20.0 times in 5.00 seconds and then stops spinning it. The salad spinner rotates 6.00 more times before it comes to rest. Assume that the spinner slows down with constant angular acceleration.

What is the angular acceleration of the salad spinner as it slows down? Express your answer numerically in radians per second per second.

2. Homework Equations
ω2f = ω20 + 2α(θ)

The Attempt at a Solution

ω = θ / t
ω = 20 * 2 * π / 5.00
ω = 8π
ω = 25.13272 radians/s

now I can solve for α using a kinematic equation:

ω2f = ω20 + 2α(θ)
02 = 25.132722 + 2 * α * (2 * π * 6.00)
0 = 631.6536 + 75.39816α
75.39816α = -631.6536
α = -8.37757 radians/s2

apparently This answer is wrong...where did I go wrong?

I used a somewhat different method and got -8π/3 rad/s², which agrees with you.

 

[Steelers72]

α =
−8
radians/s2

ANSWER 2: Deduction: -3%
α =
−8π3
radians/s2

The question only asks for the magnitude of the angular acceleration.
ANSWER 3: Deduction: -3%
α =
−8.4
radians/s2

The question only asks for the magnitude of the angular acceleration.
ANSWER 4: Deduction: -3%
α =
−2.67π
radians/s2

The question only asks for the magnitude of the angular acceleration.These were my answers. All marked wrong.

 

[SammyS]

...

These were my answers. All marked wrong.

After the first message stating that only the magnitude was asked for, it seems reasonable to give the magnitude. (The statement in the OP clearly asks for angular acceleration, no mention of magnitude.)

 

[Steelers72]

After the first message stating that only the magnitude was asked for, it seems reasonable to give the magnitude. (The statement in the OP clearly asks for angular acceleration, no mention of magnitude.)

What would be the magnitude though? I am confused as to why my answer of -8.38 radians/s^2 is wrong

 

[Chestermiller]

What would be the magnitude though? I am confused as to why my answer of -8.38 radians/s^2 is wrong

When they ask for the magnitude of a vector, they want it without the sign. The magnitude is always taken to be positive, and the sign is absorbed into the direction of the unit vector. Pretty silly to require that in the answer to this problem, however.

Chet

 

[SammyS]

... Pretty silly to require that in the answer to this problem, however.​

Chet

I agree with Chet on this point, especially since there was no mention of magnitude in the problem statement.