To find the total angular displacement during the playing time of the compact disc in part (B) of Example 10.2, the disc was modeled as a rigid object under constant angular acceleration . In reality, the angular acceleration of a disc is not constant. In this problem, let us explore the actual time dependence of the angular acceleration. (a) Assume the track on the disc is a spiral such that adjacent loops of the track are separated by a small distance h . Slum that the radius r of a given portion of the track is given by r = r i + h θ 2 π where r i is the radius of the innermost portion of the track and θ is the angle through which the disc turns to arrive at the location of the track of radius r . (b) Show that the rate of change of the angle θ is given by d θ d t = v r i + ( h θ / 2 π ) where v is the constant speed with which the disc surface passes the laser. (c) From the result in part (b), use integration to find an expression for the angle θ as a function of time. (d) From the result in part (c), use differentiation to find the angular acceleration of the disc as a function of time.
To find the total angular displacement during the playing time of the compact disc in part (B) of Example 10.2, the disc was modeled as a rigid object under constant angular acceleration . In reality, the angular acceleration of a disc is not constant. In this problem, let us explore the actual time dependence of the angular acceleration. (a) Assume the track on the disc is a spiral such that adjacent loops of the track are separated by a small distance h . Slum that the radius r of a given portion of the track is given by r = r i + h θ 2 π where r i is the radius of the innermost portion of the track and θ is the angle through which the disc turns to arrive at the location of the track of radius r . (b) Show that the rate of change of the angle θ is given by d θ d t = v r i + ( h θ / 2 π ) where v is the constant speed with which the disc surface passes the laser. (c) From the result in part (b), use integration to find an expression for the angle θ as a function of time. (d) From the result in part (c), use differentiation to find the angular acceleration of the disc as a function of time.
Solution Summary: The author explains that the radius of a given portion of the track is given by r=r_i+htheta 2pi
To find the total angular displacement during the playing time of the compact disc in part (B) of Example 10.2, the disc was modeled as a rigid object under constant angular acceleration. In reality, the angular acceleration of a disc is not constant. In this problem, let us explore the actual time dependence of the angular acceleration. (a) Assume the track on the disc is a spiral such that adjacent loops of the track are separated by a small distance h. Slum that the radius r of a given portion of the track is given by
r
=
r
i
+
h
θ
2
π
where ri is the radius of the innermost portion of the track and θ is the angle through which the disc turns to arrive at the location of the track of radius r. (b) Show that the rate of change of the angle θ is given by
d
θ
d
t
=
v
r
i
+
(
h
θ
/
2
π
)
where v is the constant speed with which the disc surface passes the laser. (c) From the result in part (b), use integration to find an expression for the angle θ as a function of time. (d) From the result in part (c), use differentiation to find the angular acceleration of the disc as a function of time.
Definition Definition Angle at which a point rotates around a specific axis or center in a given direction. Angular displacement is a vector quantity and has both magnitude and direction. The angle built by an object from its rest point to endpoint created by rotational motion is known as angular displacement. Angular displacement is denoted by θ, and the S.I. unit of angular displacement is radian or rad.
air is pushed steadily though a forced air pipe at a steady speed of 4.0 m/s. the pipe measures 56 cm by 22 cm. how fast will air move though a narrower portion of the pipe that is also rectangular and measures 32 cm by 22 cm
No chatgpt pls will upvote
13.87 ... Interplanetary Navigation. The most efficient way
to send a spacecraft from the earth to another planet is by using a
Hohmann transfer orbit (Fig. P13.87). If the orbits of the departure
and destination planets are circular, the Hohmann transfer orbit is an
elliptical orbit whose perihelion and aphelion are tangent to the
orbits of the two planets. The rockets are fired briefly at the depar-
ture planet to put the spacecraft into the transfer orbit; the spacecraft
then coasts until it reaches the destination planet. The rockets are
then fired again to put the spacecraft into the same orbit about the
sun as the destination planet. (a) For a flight from earth to Mars, in
what direction must the rockets be fired at the earth and at Mars: in
the direction of motion, or opposite the direction of motion? What
about for a flight from Mars to the earth? (b) How long does a one-
way trip from the the earth to Mars take, between the firings of the
rockets? (c) To reach Mars from the…
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