- #1
dowjonez
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A thin homogeneous rod hsa length L and mass M. Initially the rod is vertical at rest on a frictionless surface. The rod is given a slight push and begins to fall in the gravitational field.
1) write an expression for the kinetic energy T of the rod as functions of M,L,g, theta and d theta/dt
2) if y is the distance the center of mass drops. find d y/dt as a function of L, g and theta
#1)i know the Kinetic energy of the rod is given by the equation
T= 1/2 I w^2
where w = omega = d theta/dt
and I = M(L/2)^2
so T = 1/2 M(L/2)^2 d theta/dt^2
T = 1/8 M L^2 d theta/dt^2
The answer is T = 1/8 M L^2 d theta/dt^2 (Sin^2theta + 1/3)
i don't know where the (Sin^2theta + 1/3) comes from
#2)
i don't even know where to start on this one
but the answer is Y prime = sintheta sqrt ( (3gL(1-costheta) / 4-3cos^2theta)
any help would be greatly appreciated
1) write an expression for the kinetic energy T of the rod as functions of M,L,g, theta and d theta/dt
2) if y is the distance the center of mass drops. find d y/dt as a function of L, g and theta
#1)i know the Kinetic energy of the rod is given by the equation
T= 1/2 I w^2
where w = omega = d theta/dt
and I = M(L/2)^2
so T = 1/2 M(L/2)^2 d theta/dt^2
T = 1/8 M L^2 d theta/dt^2
The answer is T = 1/8 M L^2 d theta/dt^2 (Sin^2theta + 1/3)
i don't know where the (Sin^2theta + 1/3) comes from
#2)
i don't even know where to start on this one
but the answer is Y prime = sintheta sqrt ( (3gL(1-costheta) / 4-3cos^2theta)
any help would be greatly appreciated