Question

Your washing machine is spinning at 5 rev/s when you open the lid. after the lid is open the machine begins to slow down. you observe that it makes 10 revolutions before coming to a stop. assume that the angular acceleration is constant after the lid is opened.

what is the angular acceleration of the washing machine as it is coming to a stop?

Answer 1

To calculate the angular acceleration of a washing machine that slows down to a stop from 5 rev/s, making 10 revs, we use the rotational kinematic equation, convert revolutions to radians, and solve for angular acceleration, yielding an answer of α = -π rad/s².

Step-by-step explanation:

The student is asking how to calculate the angular acceleration of a washing machine as it comes to a stop. We have an initial angular velocity (ωi) of 5 rev/s, it makes 10 revolutions (rev) before stopping, and we assume constant angular acceleration (α). To solve this, we can use one of the kinematic equations for rotational motion:

ωf2 = ωi2 + 2αΘ

Where ωf is the final angular velocity (0 rev/s), ωi is the initial angular velocity (5 rev/s), α is the angular acceleration, and Θ is the angular displacement (10 rev). First, we have to convert revolutions to radians since one revolution is 2π radians. Therefore:

Θ = 10 rev × 2π rad/rev = 20π rad

Now we set ωf equal to 0 (because the washing machine stops) and solve for α:

0 = (5 rev/s × 2π rad/rev)2 + 2α(20π rad)

α = -(ωi2)/(2Θ)

α = -((5 × 2π)2)/(2 × 20π)

α = -π rad/s2

The negative sign indicates that the angular acceleration acts in the direction opposite to the motion (deceleration).