Final answer:
Linear speed is the velocity of an object along its circular path and is calculated by multiplying the radius by the angular speed (v = rω). Angular speed is the rate of change of the angular position of an object (measured in radians per second) and can be converted from revolutions per minute to radians per second by using the conversion factor 2π rad = 1 rev and dividing by 60 s/min.
Step-by-step explanation:
A student asked about the relationship between linear speed and angular speed for an object traveling in a circular path. To answer the question, it's important to recognize that linear speed (v) of an object moving in a circle is related to its angular speed (ω) and the radius (r) of the circle via the relationship v = rω. The angular speed is how fast the angle (in radians) is changing per unit of time, while linear speed is the direct speed of the object along its circular path. For example, if a particle moves 3.0 m along a circle of radius 1.5 m in 1.0 second, the linear speed is the distance traveled per time (v = 3.0 m/s) and the angular speed can be found using the formula ω = v/r, which results in 2.0 radians/second. To convert rev/min to rad/s, use the conversion factor 2π rad = 1 rev and divide by 60 seconds/min.