An electric motor turns at 2400 revolutions per minute or 2400 r/m.
Find the angular velocity, in radians per second, in exact form and in approximate form, to the nearest hundredth.
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This is what I've done so far and I don't know what to do next ...
2400 r/m divided by 60s = 40
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Answer: 80pi rad/s, 251.33 rad/s
correct.
2400 (rev/min)*(2 pi/radians/rev*(1 min/60 s)
You do the multiplying and rounding off.
Okay... ?
I don't know how to solve the problem to get the answer 80pi rad/s, 251.33 rad/s ...
Thanks drwls
To find the angular velocity in radians per second, you need to convert the revolutions per minute (RPM) to radians per second (rad/s). Here's how you can do that:
1. Start with the given value of 2400 RPM.
2. Convert RPM to revolutions per second by dividing by 60 (since there are 60 seconds in a minute). In this case, 2400 RPM ÷ 60 = 40 revolutions per second.
3. Now, to convert revolutions to radians, you multiply by 2π (since there are 2π radians in one revolution). So, 40 revolutions per second × 2π = 80π radians per second.
4. This is the exact form of the answer: 80π rad/s.
To find the approximate value to the nearest hundredth, you can approximate the value of π as 3.14 and multiply it by 80. So, 80 × 3.14 = 251.2 radians per second (rounded to the nearest tenth).
If we want to round it to the nearest hundredth, we need to look at the next digit. Since the next digit, 2, is less than 5, we keep the current value of 251.2 as the approximate form to the nearest hundredth.
Therefore, the angular velocity in radians per second, in both exact and approximate forms, is 80π rad/s and 251.20 rad/s (or 251.2 rad/s to the nearest hundredth).