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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Well, you certainly don't need to know the mass to compute that.
Since is revolves at 8.09 rpm, the plane travels
2*pi*R*8.09 = 132.2 meters, tangentially (around the circle) in 60 seconds.
Take the ratio of those two numbers and you will have the speed in meters per second.
Thanks
To find the tangential velocity, we need to first convert the rotational speed from rpm (revolutions per minute) to radians per second.
1 revolution = 2π radians
So the rotational speed in radians per second can be calculated as follows:
Rotational speed (in radians per second) = (8.09 rpm) * (2π/1 minute) * (1/60 seconds)
Next, we can find the radius of the circular path by using the length of the string. The radius (r) is half of the length of the string since the string is attached to the center of the circle.
Radius (r) = 2.60 m / 2
Finally, we can calculate the tangential velocity (v) using the formula:
Tangential velocity (v) = Rotational speed (in radians per second) * Radius (r)
Let's plug in the values and calculate the answer.