Rectangular sheets, angular velocity time?

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SUMMARY

The discussion revolves around calculating the time it takes for two identical rectangular sheets to reach the same angular velocity when subjected to the same torque, with one sheet rotating about its 0.26 m side and the other about its 0.35 m side. The first sheet achieves its final angular velocity in 7.3 seconds. To find the time for the second sheet, users are advised to calculate the moment of inertia for both orientations using the equation τ = Iα, and then apply the kinematic equation θ = 1/2(w0 + wf)*t to solve for the final angular velocity and time.

PREREQUISITES
  • Understanding of rotational dynamics, specifically torque and angular acceleration.
  • Familiarity with the moment of inertia calculations for rectangular sheets.
  • Knowledge of kinematic equations related to rotational motion.
  • Basic algebra skills for solving equations.
NEXT STEPS
  • Study the calculation of moment of inertia for different axes of rotation.
  • Learn how to apply the torque equation τ = Iα in practical scenarios.
  • Explore kinematic equations for rotational motion in-depth.
  • Practice problems involving angular velocity and time for various shapes and orientations.
USEFUL FOR

Students studying physics, particularly those focusing on rotational dynamics, as well as educators looking for examples of torque and angular motion calculations.

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Homework Statement



Two thin rectangular sheets (0.26 m 0.35 m) are identical. In the first sheet the axis of rotation lies along the 0.26 m side, and in the second it lies along the 0.35 m side. The same torque is applied to each sheet. The first sheet, starting from rest, reaches its final angular velocity in 7.3 s. How long does it take for the second sheet, starting from rest, to reach the same angular velocity?
in seconds

Homework Equations





The Attempt at a Solution



how can this be figured out?

what is the theta?

i would use this equation theta = 1/2(w0 + wf)*t

and solve for wf.

not sure what theta is in the equation though.
 
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Use the equation

\tau\ = I\alpha}

From this you will get the moment of inertia. But beware this the moment of inertia about the 0.26m side. ..you will have to find it with respect to the o.35 side.Once done that again apply the above equation.

Then apply the kinematic equation and you will get the answer.
 

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