The Physics of Throwing a Frisbee

            Earlier this week, I was talking with other members of the ultimate Frisbee teams and we were wondering how many times the Frisbee rotates if it is thrown a distance of 110 meters which is the length of a regulation Frisbee field. I thought that this question would require some physics. The average Frisbee moves at a linear speed of 14 m/s. The diameter of a Frisbee, according to the National Ultimate Association, is 0.260m. Thus, the radius of a Frisbee is 0.130m. Assuming that the disc maintains this speed for the entire of the throw, we can use this speed to determine the angular distance that the Frisbee travels using l=r𝜃

110m=0.130m𝜃

𝜃=1,100 radians.

To find out how many rotations of the Frisbee occurs, you just need to divide 1,100 radians by 2π.

Rotations= 1,100radians/2π =175 rotations of the disk in one full field throw.

My friend then asked me if the Frisbee is traveling a linear speed of 14 m/s how fast is the rotational speed of the Frisbee. You can determine the rotation of the Frisbee using the equation v=rω. If the disc is traveling at a linear speed of 14 m/s the Frisbee would have a rotation speed of:

14 m/s= 0.130mω 

108 rad/s= ω

Frisbees move pretty fast!