Find the angular velocity of the system as a function of alpha. 110 Hwa #7 M, L

Question

Find the angular velocity of the system as a function of alpha.

110 Hwa #7 M, L A disk of mass M and radius R is attached to the rod of mass M and the length L = 3R. The rod is attached to the celling at the point O such that it can (freely) rotate in a vertical plane around a fixed horizontal axis perpendicular to the rod as shown in the Figure above. The position of the system can be described by the angle between of the rod and the vertical is a (see Figure). Initially, the angle betwen the rod and vertical is 0 (as shown in the Figure above) and the ngular vecty is zero. Then, the system swings to the position of the equilibrium (at = 0) Find the angular velocity of the system as a function of . HW4 #8

Explanation / Answer

Icm of disc = M R^2 / 2

about point 0,

I1 = (M R^2 / 2) + (M (3R + R)^2) = 33 M R^2 / 2

about 0 of disc,

I2 = M L^2 / 3 = M (3 R)^2 / 3 = 3 M R^2

I = I1 + I2 = 39 M R^2 / 2

Applying energy conservation,

- M g (L/2) cos(alpha0) - Mg(L + R) cos(alpha0) + 0

= - M g (L/2) cos(alpha) - Mg(L + R) cos(alpha) + I w^2 / 2

5.5 M g R (cos(alpha) - cos(alpha0)) = (39 M R^2 / 2) w^2 /2

w = sqrt[ 22 g (cos(alpha) - cos(alpha0)) / 39 R ]

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.