Final answer:
The angular velocity of a rider on a carnival ride with a radius of 10 meters that takes 7.0 seconds for one loop is calculated using the formula ω = 2π/T. The angular velocity is 2π/7.0 radians per second. Related centripetal force problems might also require understanding the relationships between angular velocity, radius, and acceleration.
Step-by-step explanation:
The student's question pertains to finding the angular velocity of a rider on a carnival ride with a known radius and time for one complete loop. Using the formula for angular velocity ω (omega), which is ω = 2π/T, where T is the period or time for one complete revolution, the angular velocity can be calculated. Since the ride has a radius of 10 meters and takes 7.0 seconds to make one complete loop, we can substitute T with 7.0 seconds to find the angular velocity. Therefore, the angular velocity ω is 2π/7.0 radians per second.
Aside from this specific example, questions related to centripetal acceleration often involve calculating the angular velocity required for a certain acceleration at a given radius, as in the case of a rider 15.0 meters from the center of rotation experiencing 10 g of acceleration. Formulas such as ac = rω2 or ac = v2/r, where ac is the centripetal acceleration, r is the radius, ω is the angular velocity, and v is the tangential velocity, are vital.
Understanding these concepts is key to solving problems related to moment of inertia, centrifugal rides, and celestial mechanics as well, such as estimating the total distance Earth has traveled in its orbit around the Sun since its formation.