AVERAGE: 53.6/78 = 68.7%

Angular displacements are NOT 3-D vectors!! They don’t add commutatively!

Rotational Inertia for Selected objects and rotation axes: HR&W Table 10-2

Chapter 10 problems

Chapter 10 problems

Chapter 10 problems

h 2 1 h=0 CALM Q Hoop 1 Ball 2 Each m=M Hoop rolls without slipping, ball drops. [time: Ball first (24); hoop (1) same (4): Speed ball (9) hoop (11) same (7); KE ball (7), hoop (15) same (8)] The ball arrives at h=0 before the hoop. The ball is moving faster just before reaching h=0. The ball has greater kinetic energy just before it reaches h=0 because it has a very very small potential energy whereas the energy of the hoop is split between potential and kinetic [not quite] The ball is going to arrive first but they will both be moving at the same speed when they reach the floor. They will have the same kinetic energy when they reach the floor. there is no friction, so we know at least that they will both conserve energy. This means both will have equal kinetic energy at the ground [YES]. Since they both also have equal mass then they must have equal speeds (linear) [NO]. It is easy to see though that the hoop's velocity is not straight down and the ball's is, so the ball will hit first [YES].

The mass of the Earth is about 6x1024 kg and its radius is about 6x106 meters. Suppose you build a runway along the equator, line-up a million F-16's, bolt them down, and have them all fire their engines (eastward) simultaneously for 1/2 hour. Estimate the effect that would have on the rotational speed of the Earth. Assume the thrust of each plane's engine (these fighters have only one) is 30,000 lbs = 133,000 Newtons. [21 no answers; 6 confused] Total thrust= (133,000N)(1,000,000F-16's)=133,000,000,000N T(net)=I@, Frsin(&)=I@ (133,000,000,000N)(6,000,000m)sin(90)=(2/5)(6x10^24kg)(6x10^6m)^2(change w/1800s) change in angular velocity(w)=1.66x10^(-17)rad/s [20 variations on this; 6 got all the numbers correct, but this is not the right approach] I'm This would not effect the rotational speed of the earth. By the conservation of angular momentum, the jets are a pat of teh system, so the total angular momentum is unchanged. (2 got this, the atmosphere and the Earth are coupled, so the torques from the jets are internal to the system and angular momentum is indeed conserved!)

Chapter 11 problems

Rotational Inertia for Selected objects and rotation axes: HR&W Table 10-2

Chapter 11 problems

Chapter 11 Why is it “easier” to do a dive in the tuck position than the pike position? (Note: the diagram shows a dive in the pike position, not the tuck as the book suggests).

C>B>A (6); B>A>C (4); B>C>A (3); A>B>C (3) P A C B C>B>A (6); B>A>C (4); B>C>A (3); A>B>C (3) Gravity exerts the same amount of force on all three of these posts. A and B are essentially the same, and post C consists of parts that equal the hypotenuse. C›B›A, but only because of slight differences in the mass of each system, which causes the force in each to be slightly different. Each system has the same radius and angle, since the tension force from the cable is what causes the post's rotation

C>B>A (6); B>A>C (4); B>C>A (3); A>B>C (3) P A C B C>B>A (6); B>A>C (4); B>C>A (3); A>B>C (3) Gravity exerts the same amount of force on all three of these posts. A and B are essentially the same, and post C consists of parts that equal the hypotenuse. C›B›A, but only because of slight differences in the mass of each system, which causes the force in each to be slightly different. Each system has the same radius and angle, since the tension force from the cable is what causes the post's rotation In fact: A=B=C!! (neglecting mass of cable and rods)

Chapter 12 problems

Chapter 12 problems

Chapter 12 problems