Question

007 10.0 points A potter's wheel moves from rest to an angu- lar speed of 0.10 rev/s in 38.5 s. Assuming constant angular acceleration, what is its angular acceleration in rad/s2? Answer in units of rad/s. 008 10.0 points The tape in a videotape cassette has a total length 203 m and can play for 1.8 h. As the tape starts to play, the full reel has an outer radius of 47 mm and an inner radius of 14 mm. At some point during the play, both reels will have the same angular speed. What is this common angular speed? Answer in units of rad/s 009 10.0 points The driver of a car traveling at 46.9 m/s ap- plies the brakes and undergoes a constant deceleration of 2.63 m/s2 How many revolutions does each tire make before the car comes to a stop, assuming that the car does not skid and that the tires have radii of 0.45 m? Answer in units of rev.

Answer 1

007) w_f = 0.10 rev/sec = 0.10 * 2$\pi$ = 0.6283 rad/sec

w_o = 0 (starts from rest)

t = 38.5 sec

so, using rotational kinematics

w_f = $\alpha$t

$\alpha$ = 0.016 rad/sec²

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008) outer radius of the reel when the reels have the same area

r = sqrt (47² + 14² / 2) = 34.67 mm

v = 203 / 1.8 * 3600

v = 0.031327 m/s

so,

w = v/r

w = 0.031327 / 34.67e-3

w = 0.90358 rad/sec

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009) v² - u² = 2ad

d = u² / 2a

d = 418.18 m

so,

revolutions = 418.18 / 2*pi*0.45

revolutions = 147.9

revolutions = 147