is mass relevant when calculating velocity? i.e. "a merry go round rotates with angular velocity of 1 rev every 2 seconds...

asked by @parthp9 • almost 2 years ago • Physics • 5 pts

it has a radius of 5m, what is the velocity a child with mass =50 kg, who is riding a horse on the edge of the merry go round, leave answers in terms of pi"?

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1 answer

No, you do not need to know the mass to find the velocity of the child. In this case, you are simply related an angular speed (given in revolutions per second) to a linear speed (the velocity, given in m/s). All you need to relate them is the radius of the orbit (in this case, the merry go round). The equation to use is

v = rw

where w is the angular velocity (should be Greek letter omega). First, let's convert the units for angular velocity to SI units, which are radians per second. There are 2pi radians in a revolution, so

w = 1 rev / 2 s = 0.5 rev /s = 0.5 * 2pi rad/s = pi rad/s

So, the velocity of the child is

v = rw = (5 m)(pi rad/s) = 5pi m/s

Note that the units of radians disappears. A radian isn't technically a unit -- it's really just equal to 1. We often place it in the equation so we can make sense of it ourselves, but just know that I didn't magically disappear the radians. It's technically unitless.

answered by @doug • over 1 year ago