Phys. 121: Thursday, 13 Nov. HW 11: due by 5:00 pm. HW 12: ch. 16: # 16, 22, 59, and ch. 17, # 17, 20, and 46. Due date TBA (before Thanks. break). Mast. Phys.: Assign. 10 due Tues. More ex. cred. up. Reading: Finish chs. 16 and 17 by Tuesday. Exam 2: Test corr. through the OSL are available on problems 3, 4, 10, and 14; return them to me with your original exam by Tuesday. (Go to an OSL tutor; Work. 110 help session folks don't have the key.) Exam 3: will cover chapters 9, 12, 13, and sect. 10.7, and will either be a week from today (the 20th) or the following Tues. (25th; Thanksgiving week). Usual stuff is already online.

Clickers: The moon takes about 27 days to orbit the Earth once, at a distance of about 385,000 km. We can use this information to also find... a) the mass of the moon b) the mass of the sun c) the mass of the Earth d) the radius of the Earth e) the distance from the Earth to the sun

Clickers: The moon takes about 27 days to orbit the Earth once, at a distance of about 385,000 km. What is the value of Earth's g at the moon's altitude? (RE = 6.37 x 10³ km, so this is about 60 RE .) a) 9.8 m/s² , as always b) 9.8 cm/s² c) 2.8 cm/s² d) 9.8 mm/s² e) 2.8 mm/s²

a) r = 0.5 R b) r = 1.01 R c) r = 3.7 R d) r = 6.6 R e) r = 541 R Clickers: Circular orbits above the Earth have a 1-day orbit for which radius r as a multiple of Earth's radius R? (Orbits at R would take about 84 min.) a) r = 0.5 R b) r = 1.01 R c) r = 3.7 R d) r = 6.6 R e) r = 541 R

Clickers: An LED blinks once every 1/10th of a second Clickers: An LED blinks once every 1/10th of a second. The frequency of this blinking is... a) 1/10 Hz b) 1 Hz c) 10 Hz d) 1/10th s e) 10 s

Chap. 14: Oscillations Any motion which repeats itself (exactly, or nearly so) with the same time interval (T) is an example of Periodic Motion. The shortest time it takes to repeat is called the Period, denoted by T (for “Time”), measured in seconds (or minutes, hours, etc.)‏ From T, we can calculate the frequency f=1/T, and the angular frequency ω = 2 π f.

Hooke's Law (Spring Force Law): the simplest type of restoring force Now, we need to solve F = m a to find out what type of motion this causes:

Solution: Simple Harmonic Motion (SHM)‏ A = Amplitude = maximum distance on each side of equilibrium that the object moves Φ = Phase shift = adjustment for when the clock starts (t=0)‏

Slight variation: the vertical mass and spring

Another variant: the simple pendulum

Pendulum motion is simple harmonic for small amplitudes, with angular frequency

Pendulum oscillations are simple harmonic (pure sine/cosine shape) only for small angles!

Clickers: A ball on a massless, rigid rod oscillates as a simple pendulum with a period of 2.0 s. If the ball is replaced with another ball having twice the mass, the period will be 1.0 s. 1.4 s. 2.0 s. 2.8 s. 4.0 s. 13 13

Non-ideal (physical) pendulum:

A “physical” pendulum:

Clickers: A solid disk and a circular hoop have the same radius and the same mass. Each can swing back and forth as a pendulum from a pivot at one edge. Which has the larger period of oscillation? The solid disk. The circular hoop. Both have the same period. There’s not enough information to tell. 16 16

Yet another variant: the torsional oscillator (which produces actual angular oscillations): the pendulum is approximately one, for small angles. Torsional oscillators have a restoring torque, just as springs have a restoring force: τ = - κ θ

Clickers: The angular (torsional) spring constant κ has the same units as... a) an ordinary (linear) spring constant (k) b) Angle c) Force d) Torque e) Momentum

Angular version of SHM: All of the previous stuff also applies to rotational motion! We need only sub in θ for x, τ for F, I for m, and κ (torsional spring constant) for k. Result: SHM for θ, with ω² = κ/I instead of k/m.

Angular Oscillators: ω versus d θ/dt Unfortunately, we are overusing Greek letters! To tell these two concepts apart: ω is a CONSTANT, and represents the angular speed of a wheel which turns once per period of the motion. (Recall that its job is to convert time to an angle!)‏ dθ /dt is the actual angular speed of the oscillating object, and it WIGGLES WITH TIME like a sine or cosine wave; it is NOT a constant!

Another variation: a rolling mass

Clickers: A mass oscillates on a horizontal spring with period T  2.0 s. If the amplitude of the oscillation is doubled, the new period will be 1.0 s. 1.4 s. 2.0 s. 2.8 s. 4.0 s Slide 14-51 22 22

Notice that ω (and therefore also T and f)‏ is NOT adjustable; it's always the same for a given mass and spring. In contrast, both A and φ depend upon the particular motion (initial conditions).