# How Do You Calculate Angular Acceleration of a Salad Spinner?

• Steelers72
In summary, the angular acceleration of the salad spinner as it slows down is approximately -8.38 radians/s^2. While some answers may have been marked wrong for not giving the magnitude without the sign, it is not a necessary requirement for solving this problem.
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

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

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

Significant figures??

Chet

Chestermiller said:
Significant figures??

Chet
-8.0 didnt work as well.

Steelers72 said:
-8.0 didnt work as well.
-8.38??

Chet

Steelers72 said:

## 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

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

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.

α =
−8

α =
−8π3

The question only asks for the magnitude of the angular acceleration.
α =
−8.4

The question only asks for the magnitude of the angular acceleration.
α =
−2.67π

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

Steelers72 said:
...

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.)

SammyS said:
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

Steelers72 said:
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

Chestermiller said:
... 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.

## What is angular acceleration?

Angular acceleration is the rate of change of angular velocity. It is a measure of how quickly an object's angular velocity is changing over time.

## How is angular acceleration calculated?

Angular acceleration is calculated by dividing the change in angular velocity by the change in time. The units for angular acceleration are radians per second squared (rad/s^2).

## What is the difference between angular acceleration and linear acceleration?

Angular acceleration refers to the change in rotational velocity, while linear acceleration refers to the change in linear velocity. Angular acceleration is measured in radians per second squared (rad/s^2), while linear acceleration is measured in meters per second squared (m/s^2).

## What factors can affect angular acceleration?

Angular acceleration can be affected by the torque applied to an object, its moment of inertia, and any external forces acting on the object. Friction can also affect angular acceleration by slowing down the rotation of an object.

## How is angular acceleration related to angular velocity?

Angular acceleration and angular velocity are directly related. An increase in angular acceleration will result in an increase in angular velocity, and a decrease in angular acceleration will result in a decrease in angular velocity.

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