A tire 0.5m in radius rotates at a constant rate of 200 rev/min.find the speed and acceleration of a stone lodged in the tread of the tire ( on its outer edge)

zxad

To find the speed and acceleration of a stone lodged in the tread of the tire, we can use the following formulas:

1. Speed:
The speed of an object moving in a circular path is given by the formula:

Speed = Circumference × Angular Velocity

The circumference of the tire can be calculated using the formula:
Circumference = 2π × radius

The angular velocity is given as 200 rev/min. To convert it to radians per second, we need to multiply by 2π/60.

So, the formula for speed is:
Speed = (2π × radius) × (200 rev/min × 2π/60)

2. Acceleration:
The acceleration of an object moving in a circular path is given by the formula:

Acceleration = (Angular Velocity)^2 × Radius

Using the same angular velocity as before, and the given radius of the tire, we can calculate the acceleration as follows:

Acceleration = (200 rev/min × 2π/60)^2 × radius

Now, let's calculate the actual values.

Given: radius = 0.5 m

1. Speed:
Speed = (2π × 0.5) × (200 × 2π/60)
Speed ≈ 41.89 m/s

2. Acceleration:
Acceleration = (200 × 2π/60)^2 × 0.5
Acceleration ≈ 139.76 m/s²

Therefore, the speed of the stone lodged in the tread of the tire is approximately 41.89 m/s, and the acceleration is approximately 139.76 m/s².