8. Two thin rods of length L whose ends are attached to a frictionless hinge as shown in the diagram. Rod a of mass m, hangs horizontally while the rod b of mass m, hangs vertically. At time t = 0 , rod a is allowed to free fall. hinge hinge (a) Compute the angular deceleration of rod a as a fcoso function of the angle 0. [What is the torque on rod a ?] (b) Determine the angular velocity m, of rod a just before it collides with rod b. Ind = m,L² /3. (c) The two rods are identical. Prove that upon elastic collision, rod a must come to a stop (0y =0), and rod b rotates with an angular velocity as computed in part (b), that is (», = ,). Simply use the concept of conservation of angular momentum and energy for the proof. Neatness in writing your algebra expressions should help.
8. Two thin rods of length L whose ends are attached to a frictionless hinge as shown in the diagram. Rod a of mass m, hangs horizontally while the rod b of mass m, hangs vertically. At time t = 0 , rod a is allowed to free fall. hinge hinge (a) Compute the angular deceleration of rod a as a fcoso function of the angle 0. [What is the torque on rod a ?] (b) Determine the angular velocity m, of rod a just before it collides with rod b. Ind = m,L² /3. (c) The two rods are identical. Prove that upon elastic collision, rod a must come to a stop (0y =0), and rod b rotates with an angular velocity as computed in part (b), that is (», = ,). Simply use the concept of conservation of angular momentum and energy for the proof. Neatness in writing your algebra expressions should help.
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![8. Two thin rods of length L whose ends are attached to a frictionless hinge as shown in the diagram.
Rod a of mass m, hangs horizontally while the rod b of mass m, hangs vertically. At time t = 0 , rod
a is allowed to free fall.
m.
hinge
hinge
(a) Compute the angular deceleration of rod a as a
fcoso
function of the angle 0. [What is the torque on rod a ?]
(b) Determine the angular velocity o, of rod a just before
it collides with rod b. Ipmt = m,L /3.
(c) The two rods are identical. Prove that upon elastic collision, rod a must come to a stop
(@y =0), and rod b rotates with an angular velocity as computed in part (b), that is (@, = W).
Simply use the concept of conservation of angular momentum and energy for the proof. Neatness in
writing your algebra expressions should help.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7afd8d80-8c92-42e4-89fc-1bc46815ea41%2F64df5ee6-55be-430f-b025-eeb9324618ef%2F5c51npr_processed.png&w=3840&q=75)
Transcribed Image Text:8. Two thin rods of length L whose ends are attached to a frictionless hinge as shown in the diagram.
Rod a of mass m, hangs horizontally while the rod b of mass m, hangs vertically. At time t = 0 , rod
a is allowed to free fall.
m.
hinge
hinge
(a) Compute the angular deceleration of rod a as a
fcoso
function of the angle 0. [What is the torque on rod a ?]
(b) Determine the angular velocity o, of rod a just before
it collides with rod b. Ipmt = m,L /3.
(c) The two rods are identical. Prove that upon elastic collision, rod a must come to a stop
(@y =0), and rod b rotates with an angular velocity as computed in part (b), that is (@, = W).
Simply use the concept of conservation of angular momentum and energy for the proof. Neatness in
writing your algebra expressions should help.
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