Compact Disc. A compact disc (CD) stores music in a coded pattern of tiny pits 10 −7 m deep. The pits are arranged in a track that spirals outward toward the rim of the disc; the inner and outer radii of this spiral are 25.0 mm and 58.0 mm, respectively. As the disc spins inside a CD player, the track is scanned at a constant linear speed of 1.25 m/s. (a) What is the angular speed of the CD when the innermost part of the track is scanned? The outermost part of the track? (b) The maximum playing time of a CD is 74.0 min. What would be the length of the track on such a maximum-duration CD if it were stretched out in a straight line? (c) What is the average angular acceleration of a maximum-duration CD during its 74.0-min playing time? Take the direction of rotation of the disc to be positive.
Compact Disc. A compact disc (CD) stores music in a coded pattern of tiny pits 10 −7 m deep. The pits are arranged in a track that spirals outward toward the rim of the disc; the inner and outer radii of this spiral are 25.0 mm and 58.0 mm, respectively. As the disc spins inside a CD player, the track is scanned at a constant linear speed of 1.25 m/s. (a) What is the angular speed of the CD when the innermost part of the track is scanned? The outermost part of the track? (b) The maximum playing time of a CD is 74.0 min. What would be the length of the track on such a maximum-duration CD if it were stretched out in a straight line? (c) What is the average angular acceleration of a maximum-duration CD during its 74.0-min playing time? Take the direction of rotation of the disc to be positive.
Compact Disc. A compact disc (CD) stores music in a coded pattern of tiny pits 10−7 m deep. The pits are arranged in a track that spirals outward toward the rim of the disc; the inner and outer radii of this spiral are 25.0 mm and 58.0 mm, respectively. As the disc spins inside a CD player, the track is scanned at a constant linear speed of 1.25 m/s. (a) What is the angular speed of the CD when the innermost part of the track is scanned? The outermost part of the track? (b) The maximum playing time of a CD is 74.0 min. What would be the length of the track on such a maximum-duration CD if it were stretched out in a straight line? (c) What is the average angular acceleration of a maximum-duration CD during its 74.0-min playing time? Take the direction of rotation of the disc to be positive.
Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .
39. A woman stands at a horizontal distance x from a mountain
S and measures the angle of elevation of the mountaintop
above the horizontal as 0. After walking a distance di closer
to the moungain on level ground, she finds the angle to be
d. Find a general equation for the height y of the mountain
in terms of d, , and 8, neglecting the height of her eyes
above the ground.
An early method of measuring the speed of light makes use of a rotating slotted wheel. A beam of light passes through a slot at the
outside edge of the wheel, as in the figure, travels to a distant mirror, and returns to the wheel just in time to pass through the next slot
in the wheel. One such slotted wheel has a radius of 7.3 cm and 190 slots at its edge. Measurements taken when the mirror is L = 1100
m from the wheel indicate a speed of light of 3.0 x 105 km/s. (a) What is the (constant) angular speed of the wheel? (b) What is the
linear speed of a point on the edge of the wheel?
(a) Number
(b) Number
Mi
Light
Source
Units
Units
Light
beam
Rotating
slotted wheel
Mirror
perpendicular
to light beam
A vector of 6 units makes an
angle of 45 degrees with the
positive x-axis.
His vehicles are X-rays and
Z-Zs
Ax = 3.57 Ay = -4 0
%3D
%3D
Ax = 2.78 Ay = -7 0
%3D
Ax = 2.53 Ay = 2
Ax = 4.24 Ay = 4.24
%3D
%3D
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