In the figure below, a long, thin, uniform rod with a length L and a mass M is free to rotate about a horizontal pin thr

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In the figure below, a long, thin, uniform rod with alength L and a mass M is freeto rotate about a horizontal pin through one of its ends. Thefriction applied by the pin is negligible. The rod is initiallyvertical and at rest when it falls clockwise
The motion of a long, thin, uniform rod oflength L is shown onan x y plane. Initially, the rodis vertical along the positive y-axis, with the lowerend of the rod on the origin, which is labeled Pin. A clockwisearrow in the first quadrant represents the motion of the rod, andthe final position of the rod is along thepositive x-axis such that the point on the rod thatwas initially at the origin is still at the origin.
(a)
What is the angular speed of the rod at the instant it reachesthe horizontal axis? (Use any variable or symbol stated above alongwith the following as necessary: g for theacceleration of gravity.)
𝜔 =
(b)
What is the magnitude of the rod's angular acceleration at theinstant it reaches the horizontal axis? (Use any variable or symbolstated above along with the following asnecessary: g for the acceleration ofgravity.)
𝛼 =
(c)
What are the x- and y-components ofthe acceleration of the rod's center of mass at the instant itreaches the horizontal axis? (Use any variable or symbol statedabove along with the following asnecessary: g for the acceleration ofgravity.)
ax=
ay=
(d)
What are the components of the force
R
that the pin exerts on the rod at the instant the rodreaches the horizontal axis? (Use any variable or symbol statedabove along with the following asnecessary: g for the acceleration ofgravity.)Rx=
Ry=
m= a = a3​= ay​= rk​= Ry​=