Question

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$\Large \mathtt \red{Question :}$
$ \leadsto $ An engine produces $ \sf{360~ revolutions~ in ~one ~minute}$. Through how many radians will it turn in one second?

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Answer 1

$\bold \red{Answer}$

Number of revolutions made by the engine in 1 minute =360

∴ Number of revolutions made by the engine in 1 second =360/60=6

In one complete revolution, the engine turns an angle of 2π radian.

Hence, in 6 complete revolutions, it will turn an angle of 6×2π radian, i.e., 12π radian

Thus, in one second, the engine turns an angle of 12π radian.

Answer 2

Given,

→ A engine produces 360 revolutions in one minute.

we have to find :

→ How many radians will it turn in one second?

Solution :

we know that,

• 1 minute = 60 seconds.

So

$\small{ \sf \: In \: 60 \: s \: the \: engine \: produces \: 360 \: revolutions.} \\ \\ \small{ \therefore \sf \:In \:1 s \: the \: engine \: produces \: \frac{360}{60} = 6 \: \: revolutions.}$

Again,

We know that,

In 1 complete revolution, the engine produces at an angle of 2π radian.

So,

$\sf \: in \: 6 \: complete \: \: revolutions \: , \\ \small{ \sf \: it \: will \: turn \: an \: angle \: of \: = 6 \times 2\pi = 12\pi \: \: radian}$

Hence,

12π radians will it turn in one second.