A record player turntable initially rotating at 3313 rev/min is braked to a stop at a constant rotational acceleration. The turntable has a rotational inertia of 0.035 kg⋅m2 . When it is switched off, it slows down to 75% of its initial rotational speed in 5.5 s .A- How long does it take to come to rest?
B- How much work has to be done on the turntable to bring it to rest?

We have given the player turntable initially rotating at speed of [tex]33\frac{1}{3}rpm=33.333rpm=\frac{2\times 3.14\times 33.333}{60}=3.49rad/sec[/tex]

Now speed is reduced by 75 %

So final speed [tex]\frac{3.49\times 75}{100}=2.6175rad/sec[/tex]

Time t = 5.5 sec

From first equation of motion we know that '

[tex]\alpha =\frac{\omega -\omega _0}{t}=\frac{2.6175-3.49}{4}=-0.158rad/sec^2[/tex]

(a) Now final velocity [tex]\omega =0rad/sec[/tex]

So time t to come in rest [tex]t=\frac{0-3.49}{-0.158}=22sec[/tex]

(b) The work done in coming rest is given by

[tex]\frac{1}{2}I\left ( \omega ^2-\omega _0^2 \right )=\frac{1}{2}\times 0.035\times (0^2-3.49^2)=0.2131J[/tex]

topeadeniran2 topeadeniran2 · Answer 2 · 2022-03-07T12:27:31+01:00

The time taken before the object to come to rest will be 15.9986 seconds.

How to calculate the time taken

From the information given, the initial angular speed will be:

= 3313 × 2π/60

= 346.93 rad/s

The final angular speed will be:

= 0.75 × 346.93

= 260.19 rad/s

From the equation of rotational motion, the angular velocity will be:

= (260.19 - 346.93) / 4

= -21.685 rad/s²

Time taken will now be:

t = (0 - 346.93) / -21.685

t = 15.9986 seconds.

Also, the work that has to be done on the turntable to bring it to rest will be:

= 1/2 × 0.035 × 346.93²

= 2106.31 Joules.

Learn more about time taken on:

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