Question

a car tire is 57.0 cm in diameter. the car is traveling at a speed of 25.0 m/s . what is the speed of a point at the bottom edge of the tire?

Answer 1

The speed of a point at the bottom edge of the tire is 1.79 m/s.

Step-by-step explanation:

To determine the speed of a point at the bottom edge of the tire, we need to calculate the linear velocity of the tire first and then find the velocity at the bottom edge. The linear velocity of the tire can be calculated using the formula v = πd, where d is the diameter.

Given that the diameter of the tire is 57.0 cm (0.57 m) and the car is traveling at a speed of 25.0 m/s, the linear velocity of the tire is v = π × 0.57 = 1.79 m/s.

Since the point at the bottom edge of the tire is at the same distance from the center as the center of the tire (radius), the speed of the point at the bottom edge of the tire is also 1.79 m/s.

Answer 2

To calculate the speed of a point at the bottom edge of a car tire, we need to consider the rotational motion of the tire. Using the formula v = rω, where v is the linear speed, r is the radius of the tire, and ω is the angular speed, we can find the angular speed by rearranging the equation and plugging in the given values.

Step-by-step explanation:

The speed of a point at the bottom edge of a car tire can be found by considering the rotational motion of the tire. Since the car is traveling at a linear speed of 25.0 m/s, we can calculate the angular speed of the tire using the formula v = rω, where v is the linear speed, r is the radius of the tire, and ω is the angular speed.

In this case, the diameter of the car tire is given as 57.0 cm. To find the radius, we divide the diameter by 2, which gives us a radius of 28.5 cm (or 0.285 m).

Plugging in the values, we get 25.0 m/s = 0.285 m × ω. Solving for ω, the angular speed of the tire is 87.7 rad/s.