4. A pencil falls from being balanced on its tip. It has length â„“ and uni

Question

4. A pencil falls from being balanced on its tip. It has length â„“ and uniform mass m. a) Use conservation of energy to find the angular velocity of the pencil as it hits the ground. b) Use result from part a to find the velocity of the center of mass as it hits the ground. c) Compare this to the velocity of a ball dropped from a height h =â„“/2. 4. A pencil falls from being balanced on its tip. It has length â„“ and uniform mass m. a) Use conservation of energy to find the angular velocity of the pencil as it hits the ground. b) Use result from part a to find the velocity of the center of mass as it hits the ground. c) Compare this to the velocity of a ball dropped from a height h =â„“/2.

Explanation / Answer

Moment of inertia, I = Ml^2 /3 ... By conservation of energy, 1/2 I*w^2 = mgh.... 1/2 * Ml^2 /3 * w^2 = M*g*l/2.... w^2 = 3g/l .... w = sqrt(29.4/l)....

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