Question

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A gear of radius 6.1 cm turns at 11 revolutions per second. What is the linear velocity of the gear in meters per second?
v = linear velocity, d = distance traveled, and t = time.

Answer 1

Answer: 4.216 meters per second

Explanation:

Notes: Use the following conversions:

1 revolution = 2π

100 cm = 1 meter

and the following formula: v = ωr/t where v is in meters per second

`(11\ revolutions* 6.1\ cm)/(1\ second)* (2\pi)/(1\ revolution)* (1\ meter)/(100\ cm)=(1.342\pi\ meters)/(second)\\\\\\=\large\boxed{(4.216\ meters)/(second)}}`

Answer 2

Velocity = 4.22 m/s

Explanation:

Time = 1 second

Radius = 6.1 cm

Diameter = 12.2 cm = 0.122 m

Displacement = Revolution × π × Diameter

Displacement = 11 × 3.14 × 0.122

Displacement = 4.22 m

Now, Linear velocity:

Velocity = displacement / Time

Velocity = 4.22 / 1

Velocity = 4.22 m/s