a) the tip of the second hand of a clock, if the hand is 28 mm long.
b) a point of the tread of a tire of radius 18 cm, rotating 35 times per minute.
b) a point of the tread of a tire of radius 18 cm, rotating 35 times per minute.
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velocity = radius times angular velocity... v=wr
The angular velocity of a second hand is constant,
2π radians / 60 sec
= π/30 s^(-1) (radians are actually unitless because it's length/ lenght)
Now multily by your radius:
28 mm * (π/30) s^(-1) = (28π)/(30) mm/s = 14π/15 mm/s
Same for the tire. The angular velolcity is given:
35 rotatipns/min = 35* 2π radians/min = 70π/min
Now mulitply by your radius
18*70π cm/min
Also, check for your book on slader.com, they have free solutions manuals with explanations...
The angular velocity of a second hand is constant,
2π radians / 60 sec
= π/30 s^(-1) (radians are actually unitless because it's length/ lenght)
Now multily by your radius:
28 mm * (π/30) s^(-1) = (28π)/(30) mm/s = 14π/15 mm/s
Same for the tire. The angular velolcity is given:
35 rotatipns/min = 35* 2π radians/min = 70π/min
Now mulitply by your radius
18*70π cm/min
Also, check for your book on slader.com, they have free solutions manuals with explanations...