Final answer:
The question involves determining the angular velocity of a smaller wheel connected by a belt to a larger wheel with known angular velocity, within the field of high school Physics.
Step-by-step explanation:
The student's question pertains to the concept of angular velocity, which is a topic in Physics, specifically dealing with rotation and rolling motion. Given the angular speed of the larger wheel, we can relate the linear speed (tangential speed at the rim) of the belt with the angular speeds of both the larger and smaller wheels since the belt ensures that their tangential speeds are equal.
Calculating the Angular Velocity
To find the angular velocity (ω) of the smaller wheel, we use the formula v = rω, where v is the linear speed, r is the radius and ω is the angular velocity. Since the linear speed is constant across the belt, and we are given the angular speed for the larger wheel (R) and its radius, we can use the information to calculate the angular velocity for the smaller wheel (r).
The quoted material suggests using the known speed of a car tire and its radius to calculate its angular speed. We can apply a similar approach for the belt system on the air conditioner. The larger wheel's angular speed is given as 60 rpm (revolutions per minute), which can be converted to radians per second if necessary, to calculate linear speed and then the angular speed of the smaller wheel.