Finding resultant velocity from angular acceleration

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SUMMARY

The discussion focuses on calculating the resultant velocity of a rope launched by Michael, who spins the rope at an angular acceleration of 2.00 rad/s² while running at a linear acceleration of 4.00 m/s². The rope's length is 1.2 meters, and Michael takes 3 seconds before launching it. To determine the resultant velocity, one must convert angular acceleration to angular velocity and apply kinematic equations to relate angular velocity to linear velocity. The key equations discussed include the transformation from angular acceleration to angular velocity and the relationship between linear and angular motion.

PREREQUISITES
  • Understanding of angular acceleration and its units (rad/s²)
  • Familiarity with linear acceleration and its units (m/s²)
  • Knowledge of kinematic equations for linear motion
  • Basic concepts of angular motion and its relationship to linear motion
NEXT STEPS
  • Learn how to convert angular acceleration to angular velocity using the formula ω = αt
  • Study the relationship between angular velocity and linear velocity with the equation v = rω
  • Explore kinematic equations that relate linear and angular motion
  • Review examples of resultant velocity calculations in physics problems
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, as well as educators and tutors looking to clarify concepts of angular and linear motion.

Michael Fox
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Homework Statement


Michael starts spinning the rope at a rate of 2.00 rad/s^2 while he starts running towards the target at 4.00m/s^2. This distance betweens Michael's elbow and the end of the rope form a straight 1.2m segment. If Michael takes 3 seconds before he launches the rope at the target, what is the resultant velocity of the rope when it leaves Michael's hand.

Homework Equations


at= (v2-v1)/2 (i think)
at=ra (at= linear acceleration, a = angular acceleration)

The Attempt at a Solution


I believe to solve I would have to convert angular acceleration to angular velocity but I cannot figure out how to do that. Any help clarifying or a diagram would be huge. Thank you for reading
 
Physics news on Phys.org
What is the relation between angular acceleration and angular velocity? What is the relation between angular velocity and velocity?
 
You probably have some kinematic equations that can handle that "transformation".
 

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