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A wheel of radius 30.0 cm is rotating at a rate of 2.60 revolutions every 0.0510 s. Through what angle does the wheel rotate in 1.00 s?

2 Answers

2 votes

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.

User Inoyatulloh
by
8.1k points
4 votes

Answer:

the wheel rotates through approximately 18352.94 degrees in 1.00 second.

Step-by-step explanation:

User Jason Shantz
by
7.3k points