During the spin-dry cycle of a washing machine, the motor slows from 90 rad/s to 30 rad/s while the turning the drum through an angle of 180 radians. What is the magnitude of the angular acceleration of the motor? A)64 rad/s² B)32 rad/s² C)10 rad/s² D)20 rad/s² E)1.0 rad/s²

Question

Quizplus · Accepted Answer

We can use the equation for angular acceleration:

angular acceleration = (final angular velocity - initial angular velocity) / time

We are given the initial and final angular velocities, but we need to find the time it takes to slow down. We can use the equation:

Δθ = ω_i t + (1/2)αt^2

where Δθ is the angle turned, ω_i is the initial angular velocity, and α is the angular acceleration. Solving for time, we get:

t = (Δθ - (1/2) ω_i) / (ω_i - ω_f)

Substituting the given values, we get:

t = (180 rad - (1/2)(90 rad/s))(90 rad/s - 30 rad/s)

t = 3 seconds

Now we can use the equation for angular acceleration to find:

angular acceleration = (30 rad/s - 90 rad/s) / 3 s

angular acceleration = -20 rad/s^2

Taking the magnitude of this, we get:

|angular acceleration| = 20 rad/s^2

Therefore, the best choice is D, 20 rad/s^2.

During the Spin-Dry Cycle of a Washing Machine, the Motor