Answer:
1) The radius of the tire is approximately 0.28966 meters
2) The centripetal force is the force that keeps a body moving on a circular path
Explanation:
1) The linear speed of the automobile tire = 20.0 m/s
The period with which the tire turns = 0.091 s
The period = The time it takes to make a complete turn
Therefore;
The number of turns in 1 second = 1/0.091 ≈ 10.989 turns
The distance covered with 10.989 turns, assuming no friction = 10.989 × The circumference of the tire
∴ The distance covered with 10.989 turns, assuming no friction = 10.989 × 2 × π × Radius of the tire
From the speed of the car, 20.0 m/s, we have;
The distance covered in 1 second = 20.0 meters
Therefore;
10.989 × 2 × π × Radius of the tire = 20.0 meters
Radius of the tire = (20.0 meters)/(10.289 × 2 × π) ≈ 0.28966 meters
The radius of the tire ≈ 0.28966 meters
2) The centripetal force is the force required to maintain the curved motion of an object, and having a direction towards the center of the rotary motion.
The centripetal force is given by the formula,
Where;
F = The centripetal force
m = The mass of the object
v = The linear velocity of the object
r = The radius of the rotational motion.