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Home/ Questions/How many revolutions does the object make during the first 4 s?
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lyytutoria
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lyytutoriaExpert
Asked: April 13, 20222022-04-13T06:30:05+00:00 2022-04-13T06:30:05+00:00In: Physics

How many revolutions does the object make during the first 4 s?

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In the Cartesian coordinates, a figure shows the angular-velocity versus time graph for a particle moving in a circle.

y axis is the angular (rotational) speed (w) as “rad/second” and x axis is time (t) as “second”. The motion is linear in the first two seconds as:

10 rad/s at t=1

20 rad/s at t=2

Then the angular (rotational) speed is constant (w=20 rad/s) for both t=3 and t=4. here’s the graph:

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How many revolutions does the object make during the first 4 s?

♦ Relevant knowledge

An instantaneous graph of speed of rotation versus the time of a particle’s the direction of rotation is extremely useful to determine the angular displacement of the particle through evaluating areas under the graph in the two times.

revolutionrotationalspeed
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    Jake Lee
    2022-04-13T06:30:07+00:00Added an answer on April 13, 2022 at 6:30 am

    One radian equals half a turn

    If t=1s is 10 rads/s then there are 5 turns

    If t=2s it is 20 rads/s then there are 10 turns

    It is 20 rads/s at t=3s.  There are 10 turns

    It is 20 rads/s at t=4s. There are 10 turns

    There are 35 revolutions in total, which is a total of 4s.

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