Answer:
321.3 radians
Step-by-step explanation:
The first step is to calculate the angular velocity of the wheel, which is given by:
ω = 2πf
where:
ω is the angular velocity (in radians per second)
f is the frequency (in revolutions per second)
In this case, the frequency is 2.60 revolutions every 0.0510 s, or:
f = 2.60 rev / 0.0510 s = 50.98 rev/s
Converting revolutions per second to radians per second:
ω = 2π(50.98 rev/s) = 321.3 rad/s
The angle rotated by the wheel in 1.00 s is given by:
θ = ωt
where:
θ is the angle (in radians)
t is the time (in seconds)
In this case, the time is 1.00 s, so:
θ = (321.3 rad/s)(1.00 s) = 321.3 radians
Therefore, the wheel rotates through an angle of 321.3 radians in 1.00 s.