angular speed,
km/hr = m/s
cm m
A car tire has diameter 64 cm. Determine its angular velocity, in radians per second, when the car is traveling at 100 km/h.
So I want to find the number of rotations the tire makes in one second, and to do that I divide the velocity of the car by the circumference of the tire. (I think)
is the circumference of the circle in meters.
is the number of rotations per second.
So the circle makes approximately 138.5 rotations per second. I know that an entire circle is radians so I just multiple 138.5 by and that works out to be 870.22 radians/s.
The answer is supposed to be 86.83 radians/s and I don't know what I'm doing wrong. Could someone please explain?
I have no idea how to start this one. Help!Write an expression for the angular velocity, in radians per second, for a car tire with diameter d centimeters when the car is traveling at x kilometers per hour.
An alternative (but longer) method would be to make a series of multiplications of different unit ratios, from km/h to rad/s, like this:
.
That way, when multiplying out, all of the units cancel except for radians on top and seconds on bottom. I get ~86.81 rad/s as my answer.
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