How Do You Calculate Angular Velocity of a Sphere on an Incline?

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To calculate the angular velocity of a solid sphere rolling down an incline, use the conservation of energy principle, where gravitational potential energy converts into both angular and translational kinetic energy. For a sphere with mass 1.5 kg and radius 15 cm on a 35-degree incline, the relationship between linear velocity and angular velocity is given by v = rw. The total energy at the top equals the sum of translational and rotational kinetic energy at the bottom. A mathematical representation involves setting the initial potential energy equal to the final kinetic energies and solving for angular velocity.
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1. a solid sphere (I=0.4mr^2) of mass 1.5 kg and radius 15 cm moves down a 35 degrees incline 7m long. Assuming it started from rest, what is its angular velocity in rad/s at the bottom of the incline? a)71.27 b)32.25 c)49.98 d)61.69




3.i tried by plugging in the values and trying to find the angular acceleration so i could use the L=I(angular velocity) equation; but my numbers just don't add up. pls guide me through the process

thnx

ty
 
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Use the principle of conservation of Energy. The gravitational potential energy is converted into Angular Kinetic Energy.
 
The gravitational potential energy is converted into angular KE AND translational KE. Assuming that rolling without slipping happens here, you can use the relation v=rw to solve for the angular velocity.
 
can someone pls provide me with a mathematical representation of the previous replies?

or at least outline the steps that i will need to follow

im a bit confused about all this

thnx

ty
 

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