(III) Show that the total angular momentum L → = Σ r → i × p → i of a system of particles about the origin of an inertial reference frame can be written as the sum of the angular momentum about the CM, L → * (spin angular momentum), plus the angular momentum of the CM about the origin (orbital angular momentum): L → = L → * + r → CM × M v → CM . [ Hint : See the derivation of Eq. 11–9b.]
(III) Show that the total angular momentum L → = Σ r → i × p → i of a system of particles about the origin of an inertial reference frame can be written as the sum of the angular momentum about the CM, L → * (spin angular momentum), plus the angular momentum of the CM about the origin (orbital angular momentum): L → = L → * + r → CM × M v → CM . [ Hint : See the derivation of Eq. 11–9b.]
(III) Show that the total angular momentum
L
→
=
Σ
r
→
i
×
p
→
i
of a system of particles about the origin of an inertial reference frame can be written as the sum of the angular momentum about the CM,
L
→
*
(spin angular momentum), plus the angular momentum of the CM about the origin (orbital angular momentum):
L
→
=
L
→
*
+
r
→
CM
×
M
v
→
CM
. [Hint: See the derivation of Eq. 11–9b.]
Study of body parts and their functions. In this combined field of study, anatomy refers to studying the body structure of organisms, whereas physiology refers to their function.
A planet of mass m and an angular momentum L moves in a circular orbit in a potential,
V(r)=-k/r, where k is a constant. If it is slightly perturbed radially, the angular
frequency of radial oscillations is
(a) mk² / /2L3
(b) mk? / L
(c) V2mk? / L
(d) V3mk? / L
A star with mass M and radius R collides head-on with another star of mass ¾*M and radius 4/5*R, and they coalesce to form a new start at rest whose radius is 6/5*R. Assume that initially the colliding stars had angular velocities with opposite directions but the same magnitude w. What is the magnitude and direction of the final’s stars angular velocity? (Express the magnitude as a fraction of w.)
Pulsars. When a star with a mass at least ten times that of the Sun explodes outward in a supernova, its core can be collapsed into a
pulsar, which is a spinning star that emits electromagnetic radiation (radio waves or light) in two tight bears in opposite directions. If a
beam sweeps across Earth during the rotation, we can detect repeated pulses of the radiation, one per revolution. (a) The first pulsar
was discovered by Jocelyn Bell Burnell and Antony Hewish in 1967; its pulses are separated by 1.3373 s. What is its angular speed in
revolutions per second? (b) To date, the fastest spinning pulsar has an angular speed of 716 rev/s. What is the separation of its detected
pulses in milliseconds?
(a) Number
(b) Number
Hint
1345.98
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