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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.
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.