1) +x 2) x 3) +y 4) y 5) +z 6) z 7) zero magnitude

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Brett Moody
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1 Q11.1.a: What is the direction of < 0, 0, 3> x < 0, 4, 0>? 1) +x ) x 3) +y 4) y 5) +z 6) z 7) zero magnitude

2 Q11.1.b: What is the direction of < 0, 4, 0> x < 0, 0, 3>? 1) +x ) x 3) +y 4) y 5) +z 6) z 7) zero magnitude

3 Q11.1.c: What is the direction of < 0, 0, 6> x < 0, 0, -3>? 1) +x ) x 3) +y 4) y 5) +z 6) z 7) zero magnitude

4 Q11.1.d: A ball falls straight down in the xy plane. Its momentum is shown by the red arrow. What is the direction of the ball's angular momentum about location A? A 1) +x ) x 3) +y 4) y 5) +z 6) z 7) zero magnitude (z-axis points out of page)

5 Q11.1.e: A ball falls straight down in the xy plane. Its momentum is shown by the red arrow. What is the ball's z component of angular momentum about location A? A 4 m 10 kg m/s 1) +10 ) 10 3) +40 4) 40 5) 0 (z-axis points out of page)

6 Q11.1.f: A planet orbits a star, in a circular orbit in the xy plane. Its momentum is shown by the red arrow. What is the direction of the angular momentum of the planet?

7 Q11.1.g: A planet orbits a star, in a circular orbit in the xy plane. Its momentum is shown by the red arrow. 1) +x ) x 3) +y 4) y 5) +z 6) z 7) zero magnitude (z-axis points out of page)

8 Q11.1.h: A comet orbits the Sun, in an elliptical orbit in the xy plane. The red arrow indicates its momentum. Which arrow best shows the direction of the vector where A is at the center of the Sun?

9 Q11.1.i: A comet orbits the Sun, in the xy plane. Its momentum is shown by the red arrow. What is the direction of the comet's angular momentum about the Sun?

10 Q11.1.j: A comet orbits the Sun, in the xy plane. Its momentum is shown by the red arrow. What is the direction of the comet's angular momentum about the Sun? 1) +x ) x 3) +y 4) y 5) +z 6) z 7) zero magnitude (z-axis points out of page)

11 Q11.1.k: A comet orbits the Sun, in the xy plane. Its momentum is shown by the red arrow. What is the direction of the comet's angular momentum about the Sun? 1) +x ) x 3) +y 4) y 5) +z 6) z 7) zero magnitude (z-axis points out of page)

12 Q11.1.l: A comet orbits the Sun in the xz plane. Its momentum is shown by the red arrow. What is the direction of the comet's angular momentum about the Sun? 1) +x ) x 3) +y 4) y 5) +z 6) z 7) zero magnitude

13 Q11.1.m: If an object is traveling at a constant speed in a vertical circle, how does the object's angular momentum change as the object goes from the top of the circle to the bottom of the circle?

14 Q11..a: A diatomic molecule such as molecular nitrogen (N) consists of two atoms each of mass M, whose nuclei are a distance d apart. What is the moment of inertia of the molecule about its center of mass? 1) Md ) 3) 4) 5) Md 1 Md 1 Md 4 4Md d

15 Q11..b: The spokes of a bicycle wheel have low mass, so almost all of the mass of the wheel is concentrated in the rim. What is the moment of inertia of a bicycle wheel of radius R and mass M? 1) MR ) π MR 3) π RM 4) (1/) MR 5) π MR

16 Q11..c: The Earth rotates on its axis once every 4 hours. What is its angular speed? Radius: 6.4e6 m Mass: 6e4 kg 1) ω = π / (4*60*60) ) ω = π * 6.4e6 / (4*60*60) 3) ω = (6e4) * π * 6.4e6 / (4*60*60) 4) ω = (6e5) * (6.4e6) * π / (4*60*60)

17 Q11..d: The Earth orbits the Sun in a nearly circular orbit. What is its angular speed? Click any button when you have calculated the answer.

18 Q11.4.a: A yo-yo is in the xy plane. You pull up on the string with a force of magnitude 0.6 N. What is the direction of the torque you exert on the yo-yo? r = m, R= m 1) +x ) x 3) +y 4) y 5) +z 6) z 7) zero magnitude (z-axis points out of page)

19 Q11.4.b: A yo-yo is in the xy plane. You pull up on the string with a force of magnitude 0.6 N. What is the magnitude of the torque you exert? 1) N m r = m, R= m ) N m 3) 0.01 N m 4) N m 5) 0.6 N m 6) cannot be determined without knowing the length of the string

20 Q11.5.a Child runs and jumps on playground merry-goround. For the system of the child + disk (excluding the axle and the Earth), which statement is true from just before to just after impact?

21 Q11.5.b What is the initial angular momentum of the child + disk about the axle? 1) < 0, 0, 0 > ) < 0, Rmv, 0 > 3) < 0, Rmv, 0 > 4) < 0, 0, Rmv > 5) < 0, 0, Rmv >

22 Q11.7.c The disk has moment of inertia I, and after the collision it is rotating with angular speed ω. The rotational angular momentum of the disk alone (not counting the child) is 1) < 0, 0, 0 > ) < 0, Iω, 0 > 3) < 0, Iω, 0 > 4) < 0, 0, Iω > 5) < 0, 0, Iω >

23 Q11.7.d After the collision, what is the speed (in m/s) of the child? 1) ωr ) ω 3) ωr 4) ω/r 5) ω R

24 Q11.7.e After the collision, what is the translational angular momentum of the child about the axle? 1) < 0, 0, 0 > ) < 0, Rmω, 0 > 3) < 0, Rmω, 0 > 4) < 0, Rm(ωR), 0 > 5) < 0, Rm(ωR), 0 >

25 Q11.7.f (11.P.56) What principle should we use to find the final velocity of the space station? 1) The momentum principle ) The energy principle 3) The angular momentum principle

26 Q11.7.g (11.P.56) What principle should we use to find the final angular speed of the space station? 1) The momentum principle ) The energy principle 3) The angular momentum principle

27 Q11.10.a In the original Bohr model of the hydrogen atom, the electron moves in circular orbits around the proton. Apply the Momentum Principle to this model. Which of these equations is the result? )

28 Q11.10.b For the bound states of the hydrogen atom, which statement is true? 1) K+U is positive ) K+U is negative 3) K+U is zero

29 Q11.10.c: Which is the correct expression for K+U for the hydrogen atom? e = +1.6 e -19 C 1) ) 1 mv 1 mv 1 e + 4πε 0 r 1 e 4πε r 0 1 mv 1 mv 1 e + 4πε 0 r 1 e 4πε r 3) 4) 5) 0 0

30 Q11.10.d: Starting from the idea that the angular momentum of the electron is quantized, Bohr found the following for the radius of the circular orbit: r N h m = 1 e 4πε 0 What does this predict for the numerical value of r? (Leave N as a factor.) 1) r = (8.5E-30 meter)n 4) r = (5.3E-11 meter)n ) r = (5.0E+3 meter)n 5) r = (1.E-38 meter)n 3) r = (4.8E-1 meter)n

31 h = 1.05E -34 J s, m = 9E -31kg, e = 1.6E -19 C, 1 = 9E9 N m / C 4πε 0

32 Notes on answers 1) r = (8.5E-30 meter)n Didn t square the electron charge e. ) r = (5.0E+3 meter)n Didn t square h. 3) r = (4.8E-1 meter)n 1 Didn t divide by. 4πε 4) r = (5.3E-11 meter)n Correct. Useful to write as ( 0.53E - 10 meter) N 5) r = (1.E-38 meter)n Didn t divide by. 4πε e r =.

Slide 1 / 37. Rotational Motion

Slide 1 / 37. Rotational Motion Slide 1 / 37 Rotational Motion Slide 2 / 37 Angular Quantities An angle θ can be given by: where r is the radius and l is the arc length. This gives θ in radians. There are 360 in a circle or 2π radians.