A toy plane of mass 0.624 kg is flown in a circle when attached to a string. The plane moves around the circle with a rotational speed of 8.09 rpm. The length of the string is 2.60 m.

What is the tangential velocity, v, of the plane?
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To find the tangential velocity of the plane, we can use the formula:

v = ω * r

where v is the tangential velocity, ω is the angular velocity, and r is the radius of the circle.

In this case, the angular velocity is given as 8.09 rpm. However, it is more convenient to express the angular velocity in radians per second (rad/s). To convert from rpm to rad/s, we can use the following conversion factor:

1 rpm = (2π/60) rad/s

Using this conversion factor, we can find the angular velocity:

ω = 8.09 rpm * (2π/60) rad/s = 8.09 * 2π/60 rad/s

Now, we need to find the radius of the circle. The length of the string, 2.60 m, represents the circumference of the circle. Since the circumference = 2πr, we can rearrange this formula to solve for the radius:

2πr = 2.60 m

r = 2.6 m / 2π

Now, we can substitute the values into the formula for tangential velocity:

v = ω * r

v = (8.09 * 2π/60) rad/s * (2.6 m / 2π)

Simplifying the expression, we find:

v ≈ 0.854 m/s

Therefore, the tangential velocity of the toy plane is approximately 0.854 m/s.