Final answer:
To prevent a person from sliding down the wall in a rotor ride, the frictional force between the wall and the person's clothing must balance the gravitational force. We calculate the minimum angular velocity needed for this by relating the frictional force to the centripetal force required for circular motion. Key variables include the coefficient of friction, the radius of the rotor, and gravitational acceleration.
Step-by-step explanation:
Calculating Angular Velocity in a Rotor Ride
To calculate the angular velocity necessary to keep riders suspended against the wall of a rotating cylinder (such as an amusement park rotor ride), we need to understand the concepts of centripetal force and friction. The force that keeps the rider from sliding down is the frictional force between the rider's clothing and the wall of the rotor. This frictional force must be equal to the weight component of the rider that acts perpendicular to the wall for the rider to not slide. The equation for this is f = μN, where f is the frictional force, μ is the coefficient of friction, and N is the normal force.
Since the normal force in this scenario is provided by the centripetal force (which is the inward force required to keep the rider moving in a circular path), we can express it as N = m * v^2 / r, where m is the mass of the rider, v is the tangential velocity, and r is the radius of the rotor. To prevent the rider from sliding down, the frictional force must be equal to or greater than the gravitational force pulling the rider down. Therefore, for the rider to remain suspended, the condition μ * m * v^2 / r ≥ m * g must be satisfied, with g representing the acceleration due to gravity.
Solving the equation for v and converting it to angular velocity ω (since angular velocity is more commonly used in rotational systems), we have ω = v / r. By substituting the expressions into our inequality and simplifying, we find the minimum angular velocity required to keep a person suspended on a wall in terms of μ, g, and r.