Physics 3210The central-force Lagrangian is What is the Lagrangian equation of motion in r?A particle is observed to move in a spiral orbit r=kq. What is the force law that produces this orbit?A particle moves in an orbit where its radius alternately increases and decreases with time. What determines the turning points of the motion?In one transit from rmin back to rmin, an orbit moves by an angle Dq. What condition on Dq must hold if the orbit closes on itself?Physics 3210 Week 5Exam grade distributionSlide 8Which of these plots show a physically possible V(r) for the gravitational potential?For motion in gravitational potential characterized by V(r) as plotted, what type of motion corresponds to total energy E2?For motion in gravitational potential characterized by V(r) as plotted, what type of motion corresponds to total energy E1?Given the equation and the constants what is the correct way to rewrite the orbit equation?We showed that What is the correct value of e when E=Vmin?Slide 14We showed that What is the correct range of e when Vmin<E<0?Which orbit corresponds to motion with larger total energy?What is the correct value of e when E=0?Which parabolic orbit corresponds to motion with larger angular velocity (at a given angle)?What is the correct range of e when E>0?Which hyperbolic orbit corresponds to motion with larger total energy?Physics 3210Week 5 clicker questionsThe central-force Lagrangian is What is the Lagrangian equation of motion in r?A.B. C.D. ( )( )2 2 21r r U r2L = m + q -&&( )( )2r r F rm - q =&&&( )( )2r r U rm - q =&&&( )( )r r F rm - q =&&&( )( )2r r U rm - q =&&A particle is observed to move in a spiral orbit r=k. What is the force law that produces this orbit?A.B. C. ( )2 23 22kF r 1r r- � �= +� �m� �l( )2 22 22kF r 1r r- � �= +� �m� �lD. E.( )22 32F r 1r r-� �= +� �m� �l( )2 22 3kF r 1r r- � �= +� �m� �l( )23 2kF r 1r r-� �= +� �m� �lA particle moves in an orbit where its radius alternately increases and decreases with time. What determines the turning points of the motion?A.B. C. r 0=D. E.dr0dt=22d r0dt=dr0d=q22d r0d=qIn one transit from rmin back to rmin, an orbit moves by an angle . What condition on  must hold if the orbit closes on itself?A.B. C. 0Dq=D. E.2Dq= p2 a, a integerDq= p2, a integerapDq=2 a, a and b integersbpDq=Physics 3210 Week 5Wednesday clicker questionsExam grade distributionMedian = 66Standard deviation = 22Current course grade=55% exam, 45% homeworkIn one transit from rmin back to rmin, an orbit moves by an angle . What condition on  must hold if the orbit closes on itself?A.B. C. 0Dq=D. E.2Dq= p2 a, a integerDq= p2, a integerapDq=2 a, a and b integersbpDq=Which of these plots show a physically possible V(r) for the gravitational potential?A.B.C.D.For motion in gravitational potential characterized by V(r) as plotted, what type of motion corresponds to total energy E2?A. Bounded circular motion with a fixed r.B. Bounded motion between a minimum and maximum r.C. Unbounded motion with a minimum r but no maximum r.D. Unbounded motion with neither a minimum nor a maximum r.For motion in gravitational potential characterized by V(r) as plotted, what type of motion corresponds to total energy E1?A. Bounded circular motion with a fixed r.B. Bounded motion between a minimum and maximum r.C. Unbounded motion with a minimum r but no maximum r.D. Unbounded motion with neither a minimum nor a maximum r.Given the equation and the constantswhat is the correct way to rewrite the orbit equation?A.B. C. D. E.22211k rcos2E1k-mq=+mll2 222E, 1k ka = e= +m ml l=1+ cosrae qr=1+ cose qa=1 cosra- e qr=1 cos- e qar= 1+ cos- e qaWe showed that What is the correct value of  when E=Vmin?A.B. C. D. E.2min2kV2m=-l0e=1e=1e=-2e=2e=-Physics 3210 Week 5Friday clicker questionsWe showed that What is the correct range of  when Vmin<E<0?A.B. C. D. E.2min2kV2m=-l0e=1e=0 1<e <1 2<e <1 0- <e<Which orbit corresponds to motion with larger total energy?C. The orbits correspond to motion with equal energy.D. It cannot be determined from the information given.What is the correct value of  when E=0?A.B. C. D. E.0e=1e=1e=-2e=2e=-Which parabolic orbit corresponds to motion with larger angular velocity (at a given angle)?C. The orbits correspond to motion with equal angular velocity.D. It cannot be determined from the information given.What is the correct range of  when E>0?A.B. C. D. E.0e=0 1<e<1 2<e<1e>0e<Which hyperbolic orbit corresponds to motion with larger total energy?C. The orbits correspond to motion with equal energy.D. It cannot be determined from the information