Bumper Cars Bumper Cars yourself to the center of the merry - PDF document

Bumper Cars 1 Bumper Cars 2 Introductory Question Introductory Question You are riding on the edge of a spinning You are riding on the edge of a spinning � playground merry- playground merry -go go- -round. If you pull round. If you pull Bumper Cars Bumper Cars yourself to the center of the merry yourself to the center of the merry- -go go- -round, round, what will happen to its rotation? what will happen to its rotation? what will happen to its rotation? what will happen to its rotation? It will spin faster. It will spin faster. A. A. It will spin slower. It will spin slower. B. B. It will spin at the same rate. It will spin at the same rate. C. C. Bumper Cars 3 Bumper Cars 4 Observations about Bumper Cars Observations about Bumper Cars 3 Questions about Bumper Cars 3 Questions about Bumper Cars � Moving cars tend to stay moving Moving cars tend to stay moving � Does a moving bumper car carry a “force”? Does a moving bumper car carry a “force”? � � Changing a car’s motion takes time Changing a car’s motion takes time � Does a spinning bumper car carry a “torque”? Does a spinning bumper car carry a “torque”? � � Impacts alter velocities and angular velocities Impacts alter velocities and angular velocities � On an uneven floor, which way does a bumper On an uneven floor, which way does a bumper � car accelerate? car accelerate? l l ? ? � Cars often appear to exchange their motions Cars often appear to exchange their motions � The fullest cars are the hardest to redirect The fullest cars are the hardest to redirect � The least The least- -full cars get slammed during collisions full cars get slammed during collisions Bumper Cars 5 Bumper Cars 6 Question 1 Question 1 Momentum Momentum � Does a moving bumper car carry a “force”? Does a moving bumper car carry a “force”? � A translating bumper car carries momentum A translating bumper car carries momentum � � Starting and stopping a bumper car seems to Starting and stopping a bumper car seems to � Momentum Momentum � require the “investment” and “withdrawal” of require the “investment” and “withdrawal” of � is a conserved quantity (can’t create or destroy) is a conserved quantity (can’t create or destroy) some some directed some some directed directed q antity of motion What is it? directed quantity of motion. What is it? q antity of motion What is it? quantity of motion. What is it? � is a directed (vector) quantity i is a directed (vector) quantity i di di d ( d ( ) ) i i � measures the translational investment the object measures the translational investment the object needed to reach its present velocity needed to reach its present velocity momentum = mass · velocity momentum = mass · velocity 1

Bumper Cars 7 Bumper Cars 8 Exchanging Momentum Exchanging Momentum Head- Head -On Collisions On Collisions � Bumper cars exchange momentum via impulses Bumper cars exchange momentum via impulses � Bumper cars exchange momentum via impulses Bumper cars exchange momentum via impulses � � An impulse is An impulse is � The total momentum never changes The total momentum never changes � � the only way to transfer momentum the only way to transfer momentum � Car with the least mass changes velocity most Car with the least mass changes velocity most � a directed (vector) quantity a directed (vector) quantity di di d ( d ( ) ) i i � The littlest riders get creamed The littlest riders get creamed impulse = force · time impulse = force · time � When car When car 1 gives an impulse to car gives an impulse to car 2 2 , car , car 2 2 gives an gives an equal but oppositely directed impulse to car equal but oppositely directed impulse to car 1 . . Bumper Cars 9 Bumper Cars 10 Clicker Question Clicker Question Question 2 Question 2 � You pound on a nail with two different mallets, You pound on a nail with two different mallets, � Does a spinning bumper car carry a “torque”? Does a spinning bumper car carry a “torque”? one softer than the other. Their masses are equal one softer than the other. Their masses are equal � Spinning and un Spinning and un- -spinning a bumper car seems spinning a bumper car seems and you swing them equally fast. Compared to and you swing them equally fast. Compared to to require the “investment” and “withdrawal” of to require the “investment” and “withdrawal” of the harder mallet the harder mallet, the momentum transferred by , the momentum transferred by some some directed some some directed directed quantity of rotational motion. directed q antity of rotational motion quantity of rotational motion. q antity of rotational motion the softer mallet the softer mallet to the nail is to the nail is What is it? What is it? A. the same and it exerts the same force. the same and it exerts the same force. A. B. the same, but it exerts a smaller force. the same, but it exerts a smaller force. B. C. less, but it exerts the same force. less, but it exerts the same force. C. D. less and it exerts a smaller force. less and it exerts a smaller force. D. Bumper Cars 12 Newton’s Third Law Bumper Cars 11 Newton’s Third Law Angular Momentum Angular Momentum of Rotational Motion of Rotational Motion � A spinning car carries angular momentum A spinning car carries angular momentum � For every torque that one object exerts on a For every torque that one object exerts on a second object, there is an equal but oppositely second object, there is an equal but oppositely � Angular momentum Angular momentum directed torque that the second object exerts on directed torque that the second object exerts on � is a conserved quantity (can’t create or destroy) is a conserved quantity (can’t create or destroy) the first object the first object. the first object the first object. � is a directed (vector) quantity is a directed (vector) quantity i i di di d ( d ( ) ) i i � measures the rotational investment the object measures the rotational investment the object needed to reach its present angular velocity needed to reach its present angular velocity angular momentum = rotational mass· angular velocity angular momentum = rotational mass· angular velocity 2