Question

Operating speed of an automatic washing machine is 5.5 rad s-1 . After loading dirty clothes and pressing a start button, the tub of the washer can reach its operating speed with an average angular acceleration of 4.15 rad s-2 . Later at the spin-dry mode, it is starting from rest and reaching an angular speed of 6.0 revolution per second in 7.0 s. a) How long does it take for the clothes to come up to the speed during the washing mode?​

Answer 1

The rotational kinematics allows finding that the response for the time to reach the washing speed is

         t = 4.26 s

Kinematics studies the motion of bodies, in the special case that the motion is circular is called rotational kinematics.

                  θ = w₀ t + ½ α t²

Where θ is the angle, w₀ are the initial angular velocity, α is the angular acceleration and t is the time

Rotational  kinematics is written in units of radians, therefore all magnitudes must be reduced,

             θ = 6 rev ($\frac{2\pi }{1rev}$  ) = 12π rad

In this case the washing machine starts from rest, therefore the initial rotational  velocity is zero

              θ = ½ α t²

              t = $\sqrt{\frac{2 \theta}{\alpha } }$

              t = $\sqrt{\frac{2 \ 12\pi }{4.15} }$

              t = 4.26 s

In conclusion using  rotational  kinematics we can find that the answer for the time to reach the washing speed is

         t = 4.26 s

Learn more about rotational  kinematics here:

brainly.com/question/20338754