Question

A tire 0.300 m in radius rotates at a constant rate of 160 rev/min. Find the speed and acceleration of a small stone lodged in the tread of the tire (on its outer edge).

a- speed m/s
b- accelration m/s^2

Answer 1

To find the speed of the small stone lodged in the tread of the tire, use the formula v = r × ω, where v is the speed, r is the radius of the tire, and ω is the angular speed. Convert the angular speed to radians per second by multiplying by (2π radians/rev) × (1 min/60 s). Substitute the values of r and ω into the formula to find the speed of the stone.

Step-by-step explanation:

To find the speed of the small stone lodged in the tread of the tire, we can use the formula:

v = r × ω

where v is the speed, r is the radius of the tire, and ω is the angular speed.

Given that the radius of the tire is 0.300 m and the tire rotates at a constant rate of 160 rev/min, we need to convert the angular speed to radians per second. One revolution is equal to 2π radians, so the angular speed in radians per second can be calculated as:

ω = (160 rev/min) × (2π radians/rev) × (1 min/60 s)

After calculating ω, we can substitute the values of r and ω into the formula to find the speed of the stone.