Physics, 07.04.2020 18:30 adrianayepez8

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?

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Answer from: asapjvzz8786

The magnitude of the angular acceleration of the motor is $20 \;\rm rad/s^{2}$ .

Given data:

The initial angular speed of the motor is, $\omega_{1} = 90 \;\rm rad/s$ .

The final angular speed of the motor is, $\omega_{2} = 30 \;\rm rad/s$ .

The angle turned by the motor drum is, $\theta =180 \;\rm rad$ .

Here we can use the concept and fundamentals of rotational motion. We can apply the third rotational equation of motion to obtain the angular acceleration of the motor as,

$\omega^{2}_{2}=\omega^{2}_{1}+2 \alpha \theta\\\\90^{2}=30^{2}+(2 \times \alpha \times 180)\\\\\alpha = \dfrac{8100-900}{2 \times 180}\\\\\alpha =20 \;\rm rad/s^{2}$

Thus, we can conclude that the magnitude of the angular acceleration of the motor is $20 \;\rm rad/s^{2}$ .

Learn more about the angular acceleration here:

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Answer from: edgarlimon2000

The magnitude of angular acceleration of the motor is $20\ rad/s^2$ .

Explanation:

Given that,

Initial angular velocity, $\omega_i=90\ rad/s$

Final angular velocity, $\omega_f=30\ rad/s$

Angular displacement, $\theta=180\ rad$

Let $\alpha$ is the magnitude of the angular acceleration of the motor. It can be calculated using third equation of rotational kinematics as :

$\omega_f^2-\omega_i^2=2\alpha \theta\\\\\alpha =\dfrac{\omega_f^2-\omega_i^2}{2\theta}\\\\\alpha =\dfrac{30^2-90^2}{2\times 180}\\\\\alpha =-20\ rad/s^2$

So, the magnitude of angular acceleration of the motor is $20\ rad/s^2$ .

Answer from: Quest

multiple

Answer from: Quest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

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During the spin-dry cycle of a washing machine, the motor slows from 90 rad/s to 30 rad/s while the...