(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A rod with one end fixed on a smooth hinge is shown below.

The rod is released from horizontal position so that it rotates at the hinge. The mass of the rod is 800 gr and the length is 120 cm. Find:

a. the initial angular acceleration (at A)

b. the angular acceleration at B

c. angular speed at B

d. the speed of the edge of the rod at B

2. Relevant equations

KE rotation = 1/2 Iω^{2}

KE translation = 1/2 mv^{2}

PE = mgh

τ = I.α

τ = F.d

3. The attempt at a solution

The moment of inertia will be 1/3 ML^{2}

a.

τ = I.α

F.d = 1/3 ML^{2}.α

8 x 0.6 = 1/3 x 0.8 x (1.2)^{2}x α

α = 12.5 rad/s^{2}

b.

τ = I.α

8 x 0.6 sin 37° = 1/3 x 0.8 x (1.2)^{2}x α

α = 7.52 rad/s^{2}

c. don't know

d. My idea is using conservation of energy; the decrease of potential energy of the center of mass = the gain of rotational kinetic energy and translational kinetic energy

m.g.1/2 L cos 37° = 1/2 Iω^{2}+ 1/2 mv^{2}→ the question asks about v, right?

To solve for v, I have to get the ω from (c). Is my idea correct?

Thanks

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# Homework Help: Angular speed and acceleration of a rod

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