Final answer:
A tire completing 115 revolutions every 5 seconds has an angular velocity of 23π radians per second.
Step-by-step explanation:
The mentioned tire turns 115 revolutions every 5 seconds. Each revolution is a complete turn of the tire, so 115 revolutions mean the tire completes 115 full circles.
To calculate the angular velocity, which is the rate of change of the angle with time, we use the formula ω = Θ/t, where ω is the angular velocity, Θ is the angle in radians, and t is the time in seconds. Since there are 2π radians in one revolution, we multiply the number of revolutions (115) by 2π to get the angle in radians, then divide by the number of seconds (5) to find the angular velocity.
Applying the formula: ω = (115 × 2π) / 5 = 23π rad/s.
The angular velocity of the tire is 23π radians per second.