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)
6 years ago
11 months ago
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 Ć Angular Velocity
The circumference of the tire can be calculated using the formula:
Circumference = 2Ļ Ć radius
The angular velocity is given as 200 rev/min. To convert it to radians per second, we need to multiply by 2Ļ/60.
So, the formula for speed is:
Speed = (2Ļ Ć radius) Ć (200 rev/min Ć 2Ļ/60)
2. Acceleration:
The acceleration of an object moving in a circular path is given by the formula:
Acceleration = (Angular Velocity)^2 Ć 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 Ć 2Ļ/60)^2 Ć radius
Now, let's calculate the actual values.
Given: radius = 0.5 m
1. Speed:
Speed = (2Ļ Ć 0.5) Ć (200 Ć 2Ļ/60)
Speed ā 41.89 m/s
2. Acceleration:
Acceleration = (200 Ć 2Ļ/60)^2 Ć 0.5
Acceleration ā 139.76 m/sĀ²
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/sĀ².