How Many Revolutions Does a Football Make in a Perfect Spiral Pass?

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SUMMARY

The discussion focuses on calculating the number of revolutions a football makes during a perfect spiral pass thrown by a quarterback. The football spins at 7.04 revolutions per second and is thrown with a linear speed of 21.6 m/s at an angle of 47.0° from the ground. To determine the total revolutions while in the air, one must first calculate the time the football remains airborne using projectile motion equations, then apply the spin rate to find the total revolutions. The rotational kinematics equation mentioned is not correctly applied without first determining the time of flight.

PREREQUISITES
  • Understanding of projectile motion and time of flight calculations
  • Familiarity with rotational kinematics equations
  • Basic knowledge of angular velocity and its units
  • Ability to convert degrees to radians
NEXT STEPS
  • Calculate the time of flight for a projectile launched at 21.6 m/s at a 47.0° angle
  • Learn about the relationship between linear speed and angular velocity
  • Study the application of rotational kinematics in real-world scenarios
  • Explore the effects of air resistance on projectile motion
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Physics students, sports scientists, and anyone interested in the mechanics of projectile motion and rotational dynamics in sports.

leezak
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A quarterback throws a pass that is a perfect spiral. In other words, the football does not wobble, but spins smoothly about an axis passing through each end of the ball. Suppose the ball spins at 7.04 rev/s. In addition, the ball is thrown with a linear speed of 21.6 m/s at an angle of 47.0° with respect to the ground. If the ball is caught at the same height at which it left the quarterback's hand, how many revolutions has the ball made while in the air?

I translated 47.0 degrees into radians and 7.04 into radians per sec and then used the rotational kinematics equation angle theta = 1/2 (omega initial - omega) * t, and then i multiplied t by 7.04 rev/sec... what am i doing wrong?? help! thanks
 
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Start by figuring out how long the football is in the air.
 

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