Math- Trig please help!
posted by linda .
A tire with a diameter of 100 cm rotates 20 times in 3 seconds.
a) determine the angular velocity
b) how far the tire has travelled?
c) what is the speed in km/h?
a) angular velocity = 20(2π)/3 radians per second
= 40π/3 rad/sec
b) one rotation = (2π)(50) cm = 100π cm
so 20 rotations would cover 20(100π) or 2000π cm
c) assuming you mean linear speed
speed = distance / time = 2000π/3 cm/sec
= (2000π/3)(3600)/(100000) km/h
= 24π km/h
( there are 100000cm in 1 km, and 3600 seconds in 1 hour)
angular velocity is radians/sec
20rev/3sec = 20/3 rev/sec = 40pi/3 rad/sec
Assuming that the tire rolls without slipping, it has gone 20*2pi*100 = 4000pi cm
4000pi cm/3sec = 4188.8cm/sec * 3600sec/hr * 1km/100000cm = 150.8km/hr
My bad. I missed where it said diameter, not radius.
Reiny has it right.