A thin, uniform rod of length L and mass M is pivoted about one end, as shown in

Question

A thin, uniform rod of length L and mass M is pivoted about one end, as shown in the figure(Figure 1) . The rod is released from rest in a horizontal position, and allowed to swing downward without friction or air resistance.

When the rod is vertical, what is its angular speed ?

Express your answer in terms of some or all of the variables M,L, and appropriate constants.

and

When the rod is vertical, what is the tangential speed vt of its free end?

Express your answer in terms of some or all of the variables M,L, and appropriate constants.

Explanation / Answer

Given,

uniform rod of length L

mass M

applying energy conservation

drop in potential energy=gain in kinetic energy

MgL/2=0.5(ML^2/3)^2

=sqrt(3g/L)

angular speed is sqrt(3g/L)

tangential speed is

L=sqrt(3gL)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.