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Furkat [3]
3 years ago
5

When an old lp turntable was revolving at 33.3 rpm, it was shut off and uniformly slowed down and stopped in 5.5 seconds. throug

h how many rotation did it turn while stopping?
Physics
1 answer:
velikii [3]3 years ago
4 0
First, let's convert the initial angular speed from rpm (rev/min) into rad/s, keeping in mind that 1 rev = 2 \pi rad and 1 min=60 s:
\omega_i = 33  \frac{rev}{min}=33\frac{rev}{min} \cdot  \frac{2 \pi rad}{60 s}=3.45 rad/s

Now we can find the angular acceleration of the lp, keeping in mind that the final speed is zero:
\alpha =  \frac{\omega_f - \omega_i}{t}= \frac{0-3.45 rad/s}{5.5 s}=-0.63 rad/s^2
and the acceleration is negative because the LP is decelerating.

Now we can find the angle covered by the LP from the beginning to the end of its motion:
\theta (t)= \omega_i t + \frac{1}{2}\alpha t^2 = (3.45 rad/s)(5.5 s)+ \frac{1}{2}(-0.63 rad/s^2)(5.5 s)^2=
=9.45 rad

And finally, we can convert it into number of revolutions:
1 rev : 2 \pi rad = x: 9.55 rad
x= \frac{9.55}{2 \pi}= 1.52 rev
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