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Because 2? rad = 1 rev, the angular displacement in part (b) corresponds to 2.23 rev. In general, dividing the number of radians by 6 gives a good approximation to the number of revolutions, because 2? ~ 6. QUESTION If the angular acceleration were doubled for the same duration, by what factor would the angular displacement change? PRACTICE IT Use the worked example above to help you solve this problem. A compact disc rotates from rest up to an angular speed of 34.0 rad/s in a time of 0.889 s. (a) What is the angular acceleration of the disc, assuming the angular acceleration is uniform?  rad/s2 (b) Through what angle does the disc turn while coming up to speed?  rad (c) If the radius of the disc is 4.45 cm, find the tangential speed of a microbe riding on the rim of the disc.  m/s (d) What is the magnitude of the tangential acceleration of the microbe at the given time?  m/s2 EXERCISEHINTS:  GETTING STARTED  |  I'M STUCK! Use the values from PRACTICE IT to help you work this exercise. (a) What are the angular speed and angular displacement of the disc 0.350 s after it begins to rotate? ? =  rad/s   Δ? =  rad   (b) Find the tangential speed at the rim at this time.

Because 2? rad = 1 rev, the angular displacement in part (b) corresponds to 2.23 rev. In general, dividing the number of radians by 6 gives a good approximation to the number of revolutions, because 2? ~ 6. QUESTION If the angular acceleration were doubled for the same duration, by what factor would the angular displacement change? PRACTICE IT Use the worked example above to help you solve this problem. A compact disc rotates from rest up to an angular speed of 34.0 rad/s in a time of 0.889 s. (a) What is the angular acceleration of the disc, assuming the angular acceleration is uniform?  rad/s2 (b) Through what angle does the disc turn while coming up to speed?  rad (c) If the radius of the disc is 4.45 cm, find the tangential speed of a microbe riding on the rim of the disc.  m/s (d) What is the magnitude of the tangential acceleration of the microbe at the given time?  m/s2 EXERCISEHINTS:  GETTING STARTED  |  I'M STUCK! Use the values from PRACTICE IT to help you work this exercise. (a) What are the angular speed and angular displacement of the disc 0.350 s after it begins to rotate? ? =  rad/s   Δ? =  rad   (b) Find the tangential speed at the rim at this time.

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Because 2? rad = 1 rev, the angular displacement in part (b) corresponds to 2.23 rev. In general, dividing the number of radians by 6 gives a good approximation to the number of revolutions, because 2? ~ 6.

QUESTION If the angular acceleration were doubled for the same duration, by what factor would the angular displacement change?
PRACTICE IT
Use the worked example above to help you solve this problem. A compact disc rotates from rest up to an angular speed of 34.0 rad/s in a time of 0.889 s.
(a) What is the angular acceleration of the disc, assuming the angular acceleration is uniform?
 rad/s2

(b) Through what angle does the disc turn while coming up to speed?
 rad

(c) If the radius of the disc is 4.45 cm, find the tangential speed of a microbe riding on the rim of the disc.
 m/s

(d) What is the magnitude of the tangential acceleration of the microbe at the given time?
 m/s2
EXERCISEHINTS:  GETTING STARTED  |  I'M STUCK!
Use the values from PRACTICE IT to help you work this exercise.
(a) What are the angular speed and angular displacement of the disc 0.350 s after it begins to rotate?
? =  rad/s
 
Δ? =  rad
 

(b) Find the tangential speed at the rim at this time.
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