An individual's arm segment is .18m long and has an angular velocity of 117degrees/s. What is the tangential velocity of the wrist?
To determine the tangential velocity of the wrist, we need to first understand the relationship between angular velocity and tangential velocity in circular motion.
The tangential velocity of an object is the linear speed at which it moves along the circumference of a circle. It is perpendicular to the radius and directed tangent to the circular path.
Angular velocity measures the rate at which an object rotates around a fixed point. It is expressed in terms of degrees or radians per unit of time.
Now, to calculate the tangential velocity of the wrist, we can use the formula:
Tangential velocity = Angular velocity × Radius.
In this case, the radius refers to the length of the arm segment.
Given that the length of the arm segment is 0.18 meters and the angular velocity is 117 degrees per second, we can calculate the tangential velocity:
Tangential velocity = 117 degrees/s × 0.18 m
However, to perform the calculation, we need to convert the angular velocity from degrees to radians since the equation requires the angular velocity to be in radians per second.
To convert degrees to radians, remember that there are 2π radians in a circle, which corresponds to 360 degrees. Therefore, we can use the conversion factor:
1 radian = (π/180) degrees.
Now, let's convert the angular velocity to radians per second:
117 degrees/s × (π/180) radians/degree = (117π/180) radians/s.
Substituting this value into the formula, we have:
Tangential velocity = (117π/180) radians/s × 0.18 m
Finally, evaluate the expression to find the tangential velocity of the wrist.