Physics Chapter 8 – Rotational Motion Part 2

Review of Circular Motion Tangential Speed vs Rotational Speed Tangential Speed vs Rotational Speed Rotational Inertia Rotational Inertia Force vs Torque Force vs Torque Center of Mass Center of Mass

Rolling Spools

Centripetal Force Velocity involves both speed and direction.   When an object moves in a circle, even at constant speed, the object still undergoes acceleration because its direction is changing.   This change in direction is due to a net force (otherwise the object would continue to go in a straight line).   Any object moving in a circle undergoes an acceleration that is directed to the center of the circle—a centripetal acceleration.

Centripetal Force

Calculating Centripetal Force

Centripetal Force Let’s look at the can from a top-view: Let’s look at the can from a top-view:

Centripetal Force Centripetal force holds a car in a curved path. a. a.For the car to go around a curve, there must be sufficient friction to provide the required centripetal force. b. b.If the force of friction is not great enough, skidding occurs.

Centripetal Force The clothes in a washing machine are forced into a circular path, but the water is not, and it flies off tangentially.

Centripetal Force

Conical Pendulum

Banked Curves

Centrifugal Force

Centrifugal Force Effect The “centrifugal-force effect” is attributed not to any real force but to inertia—the tendency of the moving body to follow a straight-line path.

Centrifugal vs Centripetal Force If the string on the can were to break, would the can move outward? No, because there is no outward force acting on it. It would move off in a straight line tangent to its location at the moment the string broke.

Centrifugal vs Centripetal Force From the reference frame of the ladybug inside the whirling can, the ladybug is being held to the bottom of the can by a force that is directed away from the center of circular motion.

Centrifugal vs Centripetal Force From a stationary frame of reference outside the whirling can, we see there is no centrifugal force acting on the ladybug inside the whirling can. However, we do see centripetal force acting on the can, producing circular motion.

Centrifugal vs Centripetal Force Nature seen from the reference frame of the rotating system is different. In the rotating frame of reference of the whirling can, both centripetal force (supplied by the can) and centrifugal force act on the ladybug.

Centrifugal vs Centripetal Force The centrifugal force appears as a force in its own right, as real as the pull of gravity. However, there is a fundamental difference between the gravity-like centrifugal force and actual gravitational force. Gravitational force is always an interaction between one mass and another. The gravity we feel is due to the interaction between our mass and the mass of Earth.

Centrifugal vs Centripetal Force In a rotating reference frame the centrifugal force has no agent such as mass—there is no interaction counterpart. For this reason, physicists refer to centrifugal force as a fictitious force, unlike gravitational, electromagnetic, and nuclear forces. Nevertheless, to observers who are in a rotating system, centrifugal force is very real. Just as gravity is ever present at Earth’s surface, centrifugal force is ever present within a rotating system.

Check Question A heavy iron ball is attached by a spring to a rotating platform, as shown in the sketch. Two observers, one in the rotating frame and one on the ground at rest, observe its motion. Which observer sees the ball being pulled outward, stretching the spring? Which observer sees the spring pulling the ball into circular motion?

Simulated Gravity From within a rotating frame of reference, there seems to be an outwardly directed centrifugal force, which can simulate gravity.

Simulated Gravity Support Force Support Force Occupants in today’s space vehicles feel weightless because they lack a support force. Future space travelers need not be subject to weightlessness. Their space habitats will probably spin, effectively supplying a support force and simulating gravity.

Simulated Gravity   The man inside this rotating space habitat experiences simulated gravity.   As seen from the outside, the only force exerted on the man is by the floor.   As seen from the inside, there is a fictitious centrifugal force that simulates gravity.

Challenges of Simulated Gravity Variations in centripetal/centrifugal force along the radial distance. Variations in centripetal/centrifugal force along the radial distance. Human sensitivity to rotation. Human sensitivity to rotation. Large structure required Large structure required

Simulated Gravity   This NASA depiction of a rotational space colony may be a glimpse into the future.

Angular Momentum   Anything that rotates keeps on rotating until something stops it.   Recall what we learned about linear momentum:   P = linear inertia x linear velocity = m x v   Angular momentum is defined as the product of rotational inertia, I, and rotational velocity, .   angular momentum = rotational inertia × rotational velocity

Angular Momentum   Angular momentum depends on rotational velocity and rotational inertia.   The operation of a gyroscope relies on the vector nature of angular momentum.

Angular Momentum Derive the formula for angular momentum in the special case when you have a small object compared to the radial distance: Derive the formula for angular momentum in the special case when you have a small object compared to the radial distance:

Angular Momentum  Just as an external net force is required to change the linear momentum of an object.  An external net torque is required to change the angular momentum of an object. An object or system of objects will maintain its angular momentum unless acted upon by an external net torque.

Conservation of Angular Momentum   Angular momentum is conserved for systems in rotation.   The law of conservation of angular momentum states that if no unbalanced external torque acts on a rotating system, the angular momentum of that system is constant.   With no external torque, the product of rotational inertia and rotational velocity at one time will be the same as at any other time.

Conservation of Angular Momentum   When the man pulls his arms and the whirling weights inward, he decreases his rotational inertia, and his rotational speed correspondingly increases.

Conservation of Angular Momentum   Rotational speed is controlled by variations in the body’s rotational inertia as angular momentum is conserved during a forward somersault. This is done by moving some part of the body toward or away from the axis of rotation.

Example Problems