Here you need to write the total KE of the system as a SUM of the KE's for each component individually (yoke and wheel). This KE expression will involve angular velocities for each component. These angular velocities are NOT equal; however, they are related through a CONSTRAINT. The constraint here is that point A exists on each component. Write the expression for the velocity of A on the wheel and equate it to the expression for the velocity of A on the yoke. This equation will give the needed relationship between the angular velocities of the yoke and wheel.
Mar 29, 2008
Homework Hint: Problem No. 6/129
Here you need to write the total KE of the system as a SUM of the KE's for each component individually (yoke and wheel). This KE expression will involve angular velocities for each component. These angular velocities are NOT equal; however, they are related through a CONSTRAINT. The constraint here is that point A exists on each component. Write the expression for the velocity of A on the wheel and equate it to the expression for the velocity of A on the yoke. This equation will give the needed relationship between the angular velocities of the yoke and wheel.
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I am having troubles applying the radius of gyration in the Io term of the equation, could anyone give me a hint?
Appreciate it.
The mass moment of inertia about point O can be found from:
I_O = m*k_O^2
where m is the mass of the yoke (3 kg) and k_O is the radius of gyration about O ( 0.350 meters).
I am confused about which two velocities of A to relate. The origional hint states both as the wheel, and I assumed that meant a v(a)=v(o) and v(a)=v(g) equations with omegas included. But for me to finish solving, in need to also use a v(g)=v(o) equation. Is this correct, or is there a simpler method?
My goof (for not proofing what I typed).
I intended to say to equate the velocity of A on the wheel to the velocity of A on the yoke. That is, write:
v_A = v_C + omega_wheel x r_A/C
v_A = v_O + omega_yoke x rA/O
where C is the contact point of the wheel with the circular surface. Equate these to to relate omega_wheel and omega_yoke.
Sorry for the confusion created by the mistyping.
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