Circular Motion, Gravity and Orbital Motion, Rotation

Memorize the following i. For an object undergoing uniform circular motion, the net unbalanced force is directed toward the center

of the circular path (the net force is centripetal). ii. Any force which is in a direction that remains perpendicular to the direction of motion is a centripetal

force. iii. A centripetal acceleration will cause a change in the direction of an object’s velocity, but not the speed. iv. Pseudo forces, such as the coriolis effect and the centrifugal effect, appear to be real when observed

from accelerated frames of reference; in actuality, they are demonstrations of inertia. v. The centrifugal effect on an object undergoing UCM is due to the inertia of that object attempting to

continue its motion in a straight line path; the centripetal force on that object is what pulls it away from its inertial path.

vi. The Law of Universal Gravitation states that every object in the universe attracts every other object in the universe with a force that is proportional to the product of the two masses and inversely proportional to the square of the distance between them.

vii. Apparent weight, or our “sensation of weight,” is determined by the normal surface reaction force we experience at any given time.

viii. Angular acceleration (α) , angular velocity (ω) , torque (τ) , and angular momentum (L) are vector

quantities, with directions pointing along the axis of rotation. ix. An unfixed object or system will rotate around its own center of mass. x. The lever arm (r) is the radial displacement from the axis of rotation to the point of action (where the

force is applied. xi. The line of action is in both directions along the line that force is applied. xii. The magnitude of the torque is the product of the lever arm times the component of force that is

perpendicular to the lever arm: τ = r F(sinθ) xiii. Angular acceleration (α) , angular velocity (ω) , and torque (τ) are rotational vector quantities, with

directions pointing along the axis of rotation; counterclockwise rotation is defined as positive. xiv. Rotational Inertia (“moment of inertia”) is the tendency for an object to resist a change in angular

velocity; it is proportional to the objects mass and to the square of the displacement of the mass from the axis of rotation: I=∑mr2 .

xv. Rotational equilibrium is a condition where the net torque on an object is zero; the object’s angular acceleration is zero, and the object’s angular velocity remains constant.

xvi. The angular acceleration of an object or rigid system is proportional to the net torque and inversely proportional to the rotational inertia of the object or rigid system: α = τ/I

1. Uniform  Circular  Motion      

Students should understand the uniform circular motion of a particle, so they can: 1) Apply the relationships of an object’s velocity, angular velocity, centripetal acceleration, angular

acceleration, distance (arc length), angular displacement, and centripetal force. 2) Describe the direction of the particle’s velocity and acceleration at any instant during the motion. 3) Recognize the sinusoidal function of the velocity and acceleration vector components for an object

undergoing uniform circular motion; sketch or identify graphs of these quantities. 4) Determine the components of the velocity and acceleration vectors as a function of time, and 5) Analyze situations in which an object moves under the influence of one or more forces so they can

determine the magnitude and direction of the net force for objects undergoing horizontal or vertical circular motion (including mass on a rotating merry-go-round, car rounding a banked curve without friction, mass swinging on the end of a string, cart rolling down a curved track, rider on a Ferris wheel).

[Simulation “Ladybug Revolution”] http://phet.colorado.edu/en/simulation/rotation [Tutorial “Uniform Circular Motion] http://ia700200.us.archive.org/9/items/AP_Physics_B_Lesson_14/Container.html [mistake in 1st minute] 5.1: http://higheredbcs.wiley.com/legacy/college/cutnell/0471151831/sat/media/html/sat_c05/sat_c05.htm 5.2: http://higheredbcs.wiley.com/legacy/college/cutnell/0471151831/sat/media/html/sat_c05/sat_c05.htm

2. Law  of  Universal  Gravitation    Students should know Newton’s Law of Universal Gravitation, so they can:

6) Determine the force (F) that one spherically symmetrical mass exerts on another. 7) Describe the gravitational field strength (g) inside and outside a uniform sphere. 8) Determine the strength of the gravitational field at the surface or at a specified point outside a

spherically symmetrical mass. [Tutorial “Law of Gravity”] http://ia600504.us.archive.org/9/items/AP_Physics_B_Lesson_19/Container.html 4.2: gravitational force; http://higheredbcs.wiley.com/legacy/college/cutnell/0471151831/sat/media/html/sat_c04/sat_c04.htm

3. Orbits  of  planets  and  satellites    Students should demonstrate the ability to analyze orbits and other planetary motion by being able to:

9) describe qualitatively how the velocity, period of revolution, and centripetal acceleration depend upon the radius of the orbit;

10) Derive expressions for the velocity and period of revolution for a circular orbit and conclude that orbital motion does not depend on the mass of the orbiting object.

11) Derive Kepler’s Third Law for the case of circular orbits.

4. Torque  and  rotation  Students should understand the concepts of rotational motion so they can: 12) translate between quantities of rotational and linear (translational) motion 13) Calculate the torque applied by a specified constant force F on an object at a specified displacement

from a rotational point. 14) State the conditions for translational and rotational equilibrium of a rigid object. 15) solve problems of rotational equilibrium for rigid objects acted on by multiple forces applied at

varying locations. 16) Predict changes in the angular (rotational) quantities about an axis for an object when forces exerted

on the object cause a torque about that axis through an interval of time. [Simulation “Torque Ladybug”] http://phet.colorado.edu/en/simulation/torque [Simulation “Balancing Act”] http://phet.colorado.edu/en/simulation/balancing-act [Self-test 9.1 & 9.2*] http://higheredbcs.wiley.com/legacy/college/cutnell/0471151831/sat/media/html/sat_c09/sat_c09.htm [tutorial “Torque and rotational Statics”] http://ia700400.us.archive.org/27/items/AP_Physics_B_Lesson_15/Container.html