Question

A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

Answer 1

Answer:

$Number of revolutions made by the wheel in 1 second=36060=6 revolutions. As we know in one complete revolution, the wheel turns at an angle of 2π radian. Hence, in 6 complete revolutions, it will turn an angle of 6×2π radian, i.e. 12π radian. Thus, in one second, the wheel turns at an angle of 12π radian.$

Answer 2

Given,

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

1 minute = 60 seconds

Number of revolutions in 1 second = 360/60 = 6

Angle made in 1 revolution = 360°

Angles made in 6 revolutions = 6 × 360°

Radian measure of the angle in 6 revolutions = 6 × 360 × π/180

= 6 × 2 × π

= 12π

Hence, the wheel turns 12π radians in one second.