An automobile travels at 100km/h. a) Find the angular velocity of a tire with radius 36cm. b) Through what angle will the tire turn in 30s at this speed?

Question

An automobile travels at 100km/h.  a) Find the angular velocity of a tire with radius 36cm.  b) Through what angle will the tire turn in 30s at this speed?

perl · Answer

you there?

anonymous · Answer

yep

perl · Answer

ok

perl · Answer

there is a nice equation relating linear speed and angular speed (or angular velocity). 
linear velocity = radius * angular velocity (in radians). 

this comes from the equation 
s = r *theta,  divide both sides by t. 
s/t = r * theta/t , and you get the equation

anonymous · Answer

This is a bit confusing still...do you have a full solution? the answer says 77.2rad/min

perl · Answer

so we are given

perl · Answer

An automobile travels at 100km/h. a) Find the angular velocity of a tire with radius 36cm. b) Through what angle will the tire turn in 30s at this speed?

perl · Answer

so using v = r * w , where v = linear speed, r = radius, and w = angular speed in radians/ unit time. we have
100 km/h = 36 cm * w  rad/ time .

perl · Answer

now we have kilometers and centimeters, which don't cancel. but know that 110 km = 110*1000*100 cm

perl · Answer

ok so based on your solution it looks like they want radians per minute, so we have to do another conversion

anonymous · Answer

but it says angular velocity, what do you do from there?

perl · Answer

first of all, you have a mistake. you want angular velocity in radians per second

anonymous · Answer

but the answer given is 77.2r/min

perl · Answer

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