A uniform rod of mass M and length L is initially horizontal, with its left end resting on the edge of a table, and its right end being held by your hand. Suddenly, you let go of the rod. Right after its release: (a) Find the the torque on the rod calculated about its left end. (b) What is its angular acceleration α = ̈φ about its left end? (c) Determine the vertical acceleration of the rod’s center of mass.

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Question

A uniform rod of mass M and length L is initially horizontal, with its left end resting on the edge of a
table, and its right end being held by your hand. Suddenly, you let go of the rod. Right after its release: (a) Find the
the torque on the rod calculated about its left end. (b) What is its angular acceleration α = ̈φ about its left end?
(c) Determine the vertical acceleration of the rod’s center of mass. (d) Based on the previous part, what is the normal force exerted by the table on the rod? (It might help to know that the rotational inertia of a uniform rod, rotated about one end, is I = M L2/3, and that L = Iω.)

Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .

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