Posted by **linda** on Tuesday, November 29, 2011 at 4:52pm.

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?

- Math- Trig please help! -
**Reiny**, Tuesday, November 29, 2011 at 5:08pm
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)

- Math- Trig please help! -
**Steve**, Tuesday, November 29, 2011 at 5:09pm
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

- Math- oops -
**Steve**, Tuesday, November 29, 2011 at 5:11pm
My bad. I missed where it said diameter, not radius.

Reiny has it right.

- Math- Trig please help! -
**linda**, Tuesday, November 29, 2011 at 6:34pm
thank you!

- Math- Trig please help! -
**lol**, Tuesday, November 29, 2011 at 10:48pm
mori?

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