In order of fastest to slowest, how do sound waves travel through different mediums?

At time t=0 a grinding wheel has an angular velocity of 30.0 rad/s . It has a constant angular acceleration of 35.0 rad/s2 until

Rama09 [41]

Answer:

(A) 570 rad

(B) 10 s

(C) 12.5 rad/s²

Explanation:

The equations of motion for circular motions are used.

Initial angular velocity, $\omega_0 = 30.0 \text{ rad/s}$

Angular acceleration, $\alpha =35.0 \text{ rad/s}^2$

(A)

At t = 2.00 s, the angular displacement, θ, is given by

$\theta = \omega_0t+\frac{1}{2}\alpha t^2 = (30\times 2) + \frac{1}{2}\times35\times2^2=60+70 = 130\text{ rad}$

After this time, it decelerates through an angular displacement of 440 rad.

Total angular displacement = 130 + 440 rad = 570 rad

(B)

At the time the circuit breaker tips, the angular velocity is given by

$\omega = \omega_0+\alpha t = 30.0+(35.0\times 2) = 30.0+70.0 =100.0\ \text{rad/s}$

This becomes the initial angular velocity for the decelerating motion. Because it stops, the final angular velocity is 0 rad/s. The time for this part of the motion is calculated thus:

$\theta_2 = \left(\dfrac{\omega_i+\omega_f}{2}\right)t$

Here, $\theta_2=440$ (the angular displacement during deceleration)

The subscripts, i and f, on ω denote the initial and final angular velocities during deceleration.

$\omega_i = 100$

$\omega_f = 0$

$t = \dfrac{2\theta_2}{\omega_i} = \dfrac{2\times400}{100} = 8\ \text{s}$

This is the time for deceleration. The deceleration began at t = 2 s.

Hence, the wheel stops at t = 2 + 8 = 10 s.

(C)

The deceleration is given by

$\alpha_R = \dfrac{\omega_f-\omega_i}{t} = \dfrac{0-100}{8} = -12.5\text{ rad/s}^2$

The negative sign appears because it is a deceleration.

4 0

3 years ago

A basketball player spins the ball with an angular acceleration of 10 rad/s2. What is the ball’s final angular velocity if the b

Lena [83]

Explanation:

It is given that,

The angular acceleration of the basketball, $\alpha=10\ rad/s^2$

Time taken, t = 3 seconds

We need to find the ball’s final angular velocity if the ball starts from rest. It can be calculated using definition of angular acceleration i.e.

$\alpha=\dfrac{\omega_f-\omega_i}{t}$