Answer to Question #105194 in Classical Mechanics for Jefferson

Question

1. The tub of a washer goes into its spin cycle, starting from rest and gaining angular speed steadily for 8 s, at which time it is turning at 5 rev/s. At this point the person doing the laundry opens the lid, and a safety switch turns off the washer. The tub smoothly slows to rest in 12 s. Through how many revolutions does the tub turn while it is in motion?

2. A solid sphere rolls without slipping along a horizontal surface. What percentage of its total kinetic energy is rotational kinetic energy?

3. Use the parallel axis theorem to find the moment of inertia of a) solid cylinder about an axis parallel to the center of mass and passing through the edge of the cylinder and b) a hollow sphere about an axis tangent to the surface of the sphere.

Answer 1

1. As per the given question,

Let the initial angular speed$(\omega_o)$ =0

Final angular speed$(\omega)$ = 2 rev/sec

time (t) =8sec

let the angular acceleration be $\alpha$ and

Now, we know that,

$\Rightarrow \omega=\omega_o+\alpha t$

$\Rightarrow \omega=0+\alpha t$

$\alpha=\dfrac{\omega}{t}=\dfrac{2}{8}=0.25 rev/sec^2$

As per the second condition, after switched off,

After switching off, it is getting stopped in 12 sec,

$\theta=\omega t-\dfrac{\alpha t^2}{2}$

$\theta= 2\times 12-\dfrac{0.25\times 144}{2}=24-18=6$

$\theta= 2\pi n =6$

so $n=\dfrac{6}{2\pi}=\dfrac{3}{\pi}$