Pulsars—the rapidly rotating neutron stars described in Example 11.2—have magnetic fields that interact with charged particles in the surrounding interstellar medium. The result is torque that causes the pulsar’s spin rate and therefore its angular momentum to decrease very slowly. The table below gives values for the rotation period of a given pulsar as it’s been observed at the same date every 5 years for two decades. The pulsar’s rotational inertia is known to be 1.12 × 10 38 kg · m 2 . Make a plot of the pulsar’s angular momentum over time, and use the associated best-fit line, along with the rotational analog of Newton’s law, to find the torque acting on the pulsar. Year of observation 1995 2000 2005 2010 2015 Angular momentum (l0 37 kg · m 2 /s) 7.844 7.831 7.816 7.799 7.787
Pulsars—the rapidly rotating neutron stars described in Example 11.2—have magnetic fields that interact with charged particles in the surrounding interstellar medium. The result is torque that causes the pulsar’s spin rate and therefore its angular momentum to decrease very slowly. The table below gives values for the rotation period of a given pulsar as it’s been observed at the same date every 5 years for two decades. The pulsar’s rotational inertia is known to be 1.12 × 10 38 kg · m 2 . Make a plot of the pulsar’s angular momentum over time, and use the associated best-fit line, along with the rotational analog of Newton’s law, to find the torque acting on the pulsar. Year of observation 1995 2000 2005 2010 2015 Angular momentum (l0 37 kg · m 2 /s) 7.844 7.831 7.816 7.799 7.787
Pulsars—the rapidly rotating neutron stars described in Example 11.2—have magnetic fields that interact with charged particles in the surrounding interstellar medium. The result is torque that causes the pulsar’s spin rate and therefore its angular momentum to decrease very slowly. The table below gives values for the rotation period of a given pulsar as it’s been observed at the same date every 5 years for two decades. The pulsar’s rotational inertia is known to be 1.12 × 1038 kg · m2. Make a plot of the pulsar’s angular momentum over time, and use the associated best-fit line, along with the rotational analog of Newton’s law, to find the torque acting on the pulsar.
Year of observation
1995
2000
2005
2010
2015
Angular momentum
(l037 kg · m2/s)
7.844
7.831
7.816
7.799
7.787
Definition Definition Product of the moment of inertia and angular velocity of the rotating body: (L) = Iω Angular momentum is a vector quantity, and it has both magnitude and direction. The magnitude of angular momentum is represented by the length of the vector, and the direction is the same as the direction of angular velocity.
2. A projectile is shot from a launcher at an angle 0,, with an initial velocity
magnitude vo, from a point even with a tabletop. The projectile hits an apple atop a
child's noggin (see Figure 1). The apple is a height y above the tabletop, and a
horizontal distance x from the launcher. Set this up as a formal problem, and solve
for x. That is, determine an expression for x in terms of only v₁, 0, y and g.
Actually, this is quite a long expression. So, if you want, you can determine an
expression for x in terms of v., 0., and time t, and determine another expression for
timet (in terms of v., 0.,y and g) that you will solve and then substitute the value of
t into the expression for x. Your final equation(s) will be called Equation 3 (and
Equation 4).
Draw a phase portrait for an oscillating, damped spring.
A person is running a temperature of 41.0°C. What is the equivalent temperature on the Fahrenheit scale? (Enter your answer to at least three significant figures.)
°F
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