A meter stick with a mass of 0.159 k g is pivoted about one end so it can rotate

Question

A meter stick with a mass of 0.159kg    is pivoted about one end so it can rotate without friction about a horizontal axis. The meter stick is held in a horizontal position and released. As it swings through the vertical, calculate Calculate the angular speed of the stick. Calculate the linear speed of the end of the stick opposite the axis. Compare the answer in part C to the speed of a particle that has fallen 1.00m , starting from rest. A meter stick with a mass of 0.159kg    is pivoted about one end so it can rotate without friction about a horizontal axis. The meter stick is held in a horizontal position and released. As it swings through the vertical, calculate Calculate the angular speed of the stick. Calculate the linear speed of the end of the stick opposite the axis. Compare the answer in part C to the speed of a particle that has fallen 1.00m , starting from rest.

Explanation / Answer

Moment of inertia of the stick, I = 1/3 M;^2

=0.053 kg m^2

P.E converts to rotational KE

Center of mass height decreases by 1/2 m....

0.159*9.8 * (1/2) = 1/2 * 0.053 * w^2

w = 5.42 rad/s

linear speed = wr = 5.42 m/s

speed of particle = sqrt(2gh) = 4.43 m/s

Speed of end of stick is greater.

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