Question

an automobile tire turns at a rate of 10 full revolutions per second and results in a forward linear velocity of 17.8 m/s. what is the radius of the tire?

Answer 1

The radius of the tire is approximately 0.283 m.

Step-by-step explanation:

To find the radius of the tire, we can use the relationship between linear velocity and angular velocity of the tire. The linear velocity is given as 17.8 m/s and we know that the tire completes 10 full revolutions per second. We can use the formula v = rw, where v is the linear velocity, r is the radius of the tire, and w is the angular velocity.

Since the tire completes 10 full revolutions per second, the angular velocity can be calculated as 10 revolutions/second * 2π radians/revolution = 20π radians/second. Plugging in the values, we have 17.8 m/s = r * 20π radians/second. Solving for r, we get r = 17.8 m/s / (20π radians/second).

Calculating this value gives us the radius of the tire as approximately 0.283 m.

Answer 2

To determine the tire radius, the formula v = rω is used, where v is linear velocity, ω is angular velocity, and r is the radius. The tire's angular velocity is 10 full revolutions per second, converted to 20π radians per second. The radius is then calculated to be 17.8 m/s divided by 20π rad/s.

Step-by-step explanation:

To find the radius of the tire, we can use the relationship between linear velocity (v) and angular velocity (ω). The formula that connects linear velocity and angular velocity is v = rω, where v is the linear velocity, r is the radius of the tire, and ω is the angular velocity. Given that the tire makes 10 full revolutions per second, we can convert this to an angular velocity in radians per second since 1 revolution is 2π radians. So ω = 10 × 2π radians/second.

To solve for the radius, we rearrange the formula to get r = v/ω. Substituting the given values, r = 17.8 m/s / (10 × 2π rad/s) = 17.8 / (20π) meters.