Question

10.13 A bead of mass $m$ is constrained to slide along a thin, circular hoop of radius $l$ that rotates with constant angular velocity $\omega$ in a horizontal plane about a point on its rim as shown in Figure P10.13. Figure P10.13 (a) Find Lagrange's equation of motion for the bead. (b) Show that the bead oscillates like a pendulum about the point on the rim diametrically opposite the point about which the hoop rotates. (c) What is the effective \"length\" of this \"pendulum\"? 

          10.13 A bead of mass $m$ is constrained to slide along a thin, circular hoop of radius $l$ that rotates with constant angular velocity $\omega$ in a horizontal plane about a point on its rim as shown in Figure P10.13.

Figure P10.13
(a) Find Lagrange's equation of motion for the bead.
(b) Show that the bead oscillates like a pendulum about the point on the rim diametrically opposite the point about which the hoop rotates.
(c) What is the effective \"length\" of this \"pendulum\"?
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10.13 A bead of mass m is constrained to slide along a thin, circular hoop of radius l that rotates with constant angular velocity ω in a horizontal plane about a point on its rim as shown in Figure P10.13. Figure P10.13 (a) Find Lagrange's equation of motion for the bead. (b) Show that the bead oscillates like a pendulum about the point on the rim diametrically opposite the point about which the hoop rotates. (c) What is the effective l̈engthöf this p̈endulum?̈

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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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help please thanks with constant angular velocity in a horizontal plane about a point on its rim as shown in Figure P10.13. yi 6 Figure P10.13 a Find Lagrange's equation of motion for the bead. b Show that the bead oscillates like a pendulum about the point on the rim diametrically opposite the point about which the hoop rotates. e)What is the effective lengthof this pendulum?
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Transcript

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00:01 Here a conical pendulum has a mass m and it hangs from a thin rock with a length l.
00:07 Ball has initial velocity and it forms a circular motion with a speed w.
00:12 We have to find angle theta.
00:14 Let's make the sketch.
00:18 Let's show the forces which are acting.
00:20 These forces are tension, gravity and they sum results in the net force.
00:26 Here the net force is mass times centripetal acceleration.
00:31 Here let's calculate the centripetal acceleration that is omega squared radius and radius is l sin theta...
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