A car tire is 60 cm in diameter. The car is traveling at a speed of 20 m/s. (b) What is the speed of a point at the top edge of the tire?

Verified step by step guidance

1. Calculate the radius of the tire by dividing the diameter by 2. The radius (r) is half of the diameter.
2. Understand that the speed of the car (v) is the same as the linear speed of the center of the tire. This is because the center of the tire moves at the same speed as the car.
3. Recognize that the speed of a point on the top edge of the tire is the sum of the linear speed of the center and the additional linear speed due to the tire's rotation. This additional speed is equal to the linear speed of the center because the top point moves twice as fast as the center in the direction of motion.
4. Use the formula for the speed of the top edge of the tire: \(v_{\text{top}} = v + v = 2v\), where \(v\) is the linear speed of the center of the tire.
5. Substitute the given value of the car's speed into the formula to find the speed of the top edge of the tire.

Key Concepts

Linear Speed

Linear speed refers to the distance traveled per unit of time. In this context, it is the speed at which the car is moving, which is given as 20 m/s. This speed is crucial for understanding how the motion of the car translates to the motion of the tire.

Rotational Motion

Rotational motion describes how an object rotates around an axis. For the tire, as it rolls, different points on its circumference move in circular paths. The relationship between linear speed and rotational speed is essential for determining the speed of points on the tire's surface.

Tangential Speed

Tangential speed is the linear speed of a point on the edge of a rotating object. For the tire, the speed of a point at the top edge can be calculated by adding the linear speed of the car to the rotational speed of the tire. This concept is key to solving the problem, as it combines both the car's speed and the tire's rotation.