if a tire is out of round so that the radius in a certain direction is 1 inch more than in the opposite direction, what is the difference in linear speed between these two points on the tire? Angular speed is 40 radians per second
To find the difference in linear speed between two points on the tire, we need to understand the relationship between linear speed and angular speed.
Linear speed is the distance traveled by an object per unit of time, while angular speed is the rate at which an object rotates or travels along a circular path.
The linear speed of a point on a rotating object can be calculated using the formula:
Linear Speed = Angular Speed × Radius
In this case, we are given that the angular speed is 40 radians per second. However, since the tire is out of round, the radius is not the same in all directions.
Let's assume that the radius in one direction (let's call it direction A) is r inches, and in the opposite direction (direction B), it is r + 1 inch.
Using the formula above, we can calculate the linear speed for each direction:
Linear Speed in Direction A = Angular Speed × Radius in A
Linear Speed in Direction B = Angular Speed × Radius in B
Substituting the given values into the formulas, we get:
Linear Speed in Direction A = 40 radians/second × r inches
Linear Speed in Direction B = 40 radians/second × (r + 1) inches
To find the difference in linear speed between the two points, we subtract the linear speed in direction B from the linear speed in direction A:
Difference in Linear Speed = Linear Speed in Direction A - Linear Speed in Direction B
Substituting the formulas above into the equation, we get:
Difference in Linear Speed = (40 radians/second × r inches) - (40 radians/second × (r + 1) inches)
Simplifying the equation, we have:
Difference in Linear Speed = 40 radians/second × (r inches - (r + 1) inches)
= 40 radians/second × (r - r - 1) inches
= 40 radians/second × (-1) inch
= -40 radians/second × 1 inch
Therefore, the difference in linear speed between the two points on the tire is -40 inches per second. Note that the negative sign indicates that the linear speed in direction B is greater than the linear speed in direction A, due to the larger radius.
linear speed1= r1*angular speed
linear speed2= r2*angular speed
difference= (r1-r1)angular speed