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3 years ago

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A record turntable rotates through 5.0 rad in 2.8 s as it is accelerated uniformly from rest. What is the angular velocity at th

e end of that time?

1 answer:

mr_godi [17]3 years ago

4 0

Answer:

$\omega_f = 3.584\ rad/s$

Explanation:

given,

turntable rotate to, θ = 5 rad

time, t = 2.8 s

initial angular speed = 0 rad/s

final angular speed = ?

now, using equation of rotational motion

$\theta = \omega_i t + \dfrac{1}{2}\alpha t^2$

$5 = 0+ \dfrac{1}{2}\alpha\times 2.8^2$

$\alpha= \dfrac{10}{2.8^2}$

α = 1.28 rad/s²

now, calculation of angular velocity

$\omega_f = \omega_i + \alpha t$

$\omega_f =0 +1.28\times 2.8$

$\omega_f = 3.584\ rad/s$

hence, the angular velocity at the end is equal to 3.584 rad/s

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<h3>How to determine the angular velocity of a collar</h3>

In this question we have a system formed by three elements, the element AB experiments a <em>pure</em> rotation at <em>constant</em> velocity, the element BD has a <em>general plane</em> motion, which is a combination of rotation and traslation, and the ruff experiments a <em>pure</em> translation.

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<h3>Accelerations</h3>

$a_{D}+\alpha_{BD}\cdot \sin \gamma = -\omega_{AB}^{2}\cdot r_{AB}\cdot \cos \theta -\alpha_{AB}\cdot r_{AB}\cdot \sin \theta - \omega_{BD}^{2}\cdot r_{BD}\cdot \cos \gamma$ (3)

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<h3>Remark</h3>

The statement is incomplete and figure is missing, complete form is introduced below:

<em>Arm AB has a constant angular velocity of 16 radians per second counterclockwise. At the instant when θ = 60°, determine the acceleration of collar D.</em>

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