Case 1: A DJ starts up her phonograph player. The turntable accelerates uniformly from rest, and takes t1 = 11.6 seconds to get up to its full speed of f1 = 78 revolutions per minute. Case 2: The DJ then changes the speed of the turntable from f1 = 78 to f2 = 120 revolutions per minute. She notices that the turntable rotates exactly n2= 12 times while accelerating uniformly. t1 = 11.6 seconds n2 = 12 times a. Calculate the angular speed described in Case 1, given as f1 = 78 revolutions per minute, into units of radians/second. b. How many revolutions does the turntable make while accelerating in Case 1? c. Calculate the magnitude of the angular acceleration of the turntable in Case 1, in radians/second2. d. Calculate the magnitude of the angular acceleration of the turntable (in radians/second2) while increasing to 120 RPM (Case 2).
Case 1: A DJ starts up her phonograph player. The turntable accelerates uniformly from rest, and takes t1 = 11.6 seconds to get up to its full speed of f1 = 78 revolutions per minute. Case 2: The DJ then changes the speed of the turntable from f1 = 78 to f2 = 120 revolutions per minute. She notices that the turntable rotates exactly n2= 12 times while accelerating uniformly. t1 = 11.6 seconds n2 = 12 times a. Calculate the angular speed described in Case 1, given as f1 = 78 revolutions per minute, into units of radians/second. b. How many revolutions does the turntable make while accelerating in Case 1? c. Calculate the magnitude of the angular acceleration of the turntable in Case 1, in radians/second2. d. Calculate the magnitude of the angular acceleration of the turntable (in radians/second2) while increasing to 120 RPM (Case 2).
Case 1: A DJ starts up her phonograph player. The turntable accelerates uniformly from rest, and takes t1 = 11.6 seconds to get up to its full speed of f1 = 78 revolutions per minute. Case 2: The DJ then changes the speed of the turntable from f1 = 78 to f2 = 120 revolutions per minute. She notices that the turntable rotates exactly n2= 12 times while accelerating uniformly. t1 = 11.6 seconds n2 = 12 times a. Calculate the angular speed described in Case 1, given as f1 = 78 revolutions per minute, into units of radians/second. b. How many revolutions does the turntable make while accelerating in Case 1? c. Calculate the magnitude of the angular acceleration of the turntable in Case 1, in radians/second2. d. Calculate the magnitude of the angular acceleration of the turntable (in radians/second2) while increasing to 120 RPM (Case 2).
Case 1: A DJ starts up her phonograph player. The turntable accelerates uniformly from rest, and takes t1 = 11.6 seconds to get up to its full speed of f1 = 78 revolutions per minute.
Case 2: The DJ then changes the speed of the turntable from f1 = 78 to f2 = 120 revolutions per minute. She notices that the turntable rotates exactly n2= 12 times while accelerating uniformly.
t1 = 11.6 seconds n2 = 12 times
a. Calculate the angular speed described in Case 1, given as f1 = 78 revolutions per minute, into units of radians/second.
b. How many revolutions does the turntable make while accelerating in Case 1?
c. Calculate the magnitude of the angular acceleration of the turntable in Case 1, in radians/second2.
d. Calculate the magnitude of the angular acceleration of the turntable (in radians/second2) while increasing to 120 RPM (Case 2).
e. How long (in seconds) does it take for the turntable to go from f1 = 78 to f2 = 120 RPM?
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 .
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Case 1: A DJ starts up her phonograph player. The turntable accelerates uniformly from rest, and takes t1 = 11.6 seconds to get up to its full speed of f1 = 78 revolutions per minute.
Case 2: The DJ then changes the speed of the turntable from f1 = 78 to f2 = 120 revolutions per minute. She notices that the turntable rotates exactly n2= 12 times while accelerating uniformly.
t1 = 11.6 seconds n2 = 12 times
d. Calculate the magnitude of the angular acceleration of the turntable (in radians/second2) while increasing to 120 RPM (Case 2).
e. How long (in seconds) does it take for the turntable to go from f1 = 78 to f2 = 120 RPM?
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