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bikkja
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Rolling sphere, problems with the fundementals.
A sphere with the mass of 2.5 kg rolls without slipping. The speed of the center of gravity is 10 m/s.
a) Calculate the translational kinetic energy of the sphere
b) Calculate the rotational energy of the sphere
c) Calculate the total kinetic energy of the sphere
d) Repeat a)-c) for a hollow cylinder with the same mass and speed
vT = ω x r ,where vT is the speed of the center of gravity for the sphere
Er = 1/2 x I x ω^2 , where Er is the rotational energy and ω=angular velocity
I = 2/5 x M x r^2 , moment of inertia of the ball
Ek = 1/2 x m x vT^2 + 1/2 x I x ω^2 , where Ek is the total kinetic energy of the rolling motion
My first thought was finding the radius using vT=ω x r , my book says that ω=2 rad/s
r = (10 m/s)/(2 rad/s) = 10/2pi m, but I am really not sure if I am allowed to do this. I can't find any examples in my textbook that relates to this problem.
Homework Statement
A sphere with the mass of 2.5 kg rolls without slipping. The speed of the center of gravity is 10 m/s.
a) Calculate the translational kinetic energy of the sphere
b) Calculate the rotational energy of the sphere
c) Calculate the total kinetic energy of the sphere
d) Repeat a)-c) for a hollow cylinder with the same mass and speed
Homework Equations
vT = ω x r ,where vT is the speed of the center of gravity for the sphere
Er = 1/2 x I x ω^2 , where Er is the rotational energy and ω=angular velocity
I = 2/5 x M x r^2 , moment of inertia of the ball
Ek = 1/2 x m x vT^2 + 1/2 x I x ω^2 , where Ek is the total kinetic energy of the rolling motion
The Attempt at a Solution
My first thought was finding the radius using vT=ω x r , my book says that ω=2 rad/s
r = (10 m/s)/(2 rad/s) = 10/2pi m, but I am really not sure if I am allowed to do this. I can't find any examples in my textbook that relates to this problem.
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