Angular displacement of a curve ball

[jmgXD6]

1. A pitcher throws a curveball that reaches the catcher in .60s. The ball is spinning at an average angular velocity of 330 rev/min, (assumed constant) on the path to the catcher's mitt. Find angular displacement. 2. θ=ωt where t is time, ω is angular velocity, and θ is angular displacement.

3. I converted 330 rpm into revs/sec and got 5.5. I then multiplied 5.5 by .6 and got 3.3 plugged in the equation and had 3.3 radian as the answer but it's not an answer choice, the closest to it is 5.8 rad. What am I doing wrong?

 

[Alucinor]

Check out your units.

You have a ball spinning rev/min. You converted it to rev/sec. Then you converted it to rev by multiplying by time. However you want your answer to be in radians. How many radians are in a rev? (It'd be 360 for degrees)

The question doesn't seem to be asking how much the ball deviates from a straight path, but if that is what you want you'd need some more information and the Magnus Effect. However I don't think that is what the question is asking based off of what you've given.

 

[jmgXD6]

2π in a circle

 

[Alucinor]

That's right, so using that to convert to radians should give you the answer you're looking for.

 

[jmgXD6]

Alright so I multiply 5.5 by 2*pi and I got 34.557 then I multiply that by 0.6 and got 20.7, which is close to 21 rad. However it asked for angular displacement of the baseball as it's travels from the pitcher to the catcher. So how would I use Magnus effect to find the angular displacement?

 

[Alucinor]

Angular displacement would be the amount that it rotates through on an axis, so that 20.7 rad is what you would be looking for

 

[jmgXD6]

Alright, thank you very much for your help.

 

[nalaing]

The one that you should be looking for is the 20.7 rad. The amount that it rotates is the angular displacement. Anyway I was wondering on the concept of throwing a curve ball. http://www.fastarm.com/2012/03/26/how-to-throw-a-curveball-using-the-fastarm/ if you are also interested on throwing a curve ball. Does the throw have different effect if a left handed throw it?

 

[ben682]

does anyone know where i can get a derivation of the magnus effect, i haven't been able to find it anywhere