Question

A flywheel is rotating at 30 rev/s. What is the total angle, in radians, through which a point on the flywheel rotates in 40 s?

a) 750π rad
b) 800π rad
c) 1200π rad
d) 1440π rad

Answer 1

The total angle through which a point on the flywheel rotates in 40 seconds is 2400π radians (option d).

Step-by-step explanation:

Angular velocity can be calculated using the formula:

ω = 2πf

where ω is the angular velocity in radians per second and f is the frequency in revolutions per second. In this case, the flywheel is rotating at 30 rev/s, so:

ω = 2π(30) = 60π rad/s

The total angle a point on the flywheel rotates through in 40 seconds can be calculated using the formula:

θ = ωt

where θ is the total angle in radians, ω is the angular velocity in radians per second, and t is the time in seconds. Substituting the values:

θ = (60π)(40) = 2400π rad

Therefore, the total angle through which a point on the flywheel rotates in 40 seconds is 2400π radians (option d).