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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?

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.