Answer :
Final answer:
The angular speed of the car tire traveling at a linear speed of 90 km/hr and with a radius of 38.4 cm is approximately 65.1 rad/s.
Explanation:
The question is asking for the angular speed of a car tire, given the linear speed of the car and the tire radius. To find this, we can use the relationship between linear and angular speed given by the formula v = rw, where v is the linear speed, r is the radius and w is the angular speed.
The given linear speed of the car is 90.0 km/hr. To convert this into SI units (meters per second), we multiply by 1000 to convert kilometers to meters and divide by 3600 to convert hours to seconds, which gives us 25 m/s. The radius of the tire (given in cm) must also be converted into meters by dividing by 100, resulting in a radius of 0.384 meters.
Substitute the values into the formula v =rw, we rearrange it to w = v/r to get angular speed. Dividing the linear speed (25 m/s) by the radius (0.384 m) gives an angular speed of approximately 65.1 rad/s.
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