10/13/11. How many degrees in 1 radian?

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1 Reading quiz! How many degrees in 1 radian? Physics 101 Tuesday 10/13/11 Class 15" Chapter " Rocket problems" Angular position, velocity and acc" Rotational Kinematics and Connection with linear Kin." Rolling motion" A) 1 rad = 2 o B) 1 rad = 180 o C) 1 rad = 10 o D) 1 rad = 57.3 o E) Radian is not a measure of angle, so the question makes no sense. Center of Mass! Rocket problems!! F =!! p!t =!m! v!t But we can do: You are used to:! F =!!! p!t = v!m!t! F =!! p!t = m!! v!t A 0.10kg Bucket sits on a scale, into this bucket you pour sand at a constant rate of 500. g/s. If the sand lands in the bucket with a speed of 3.0 m/s, what is the reading on the scale when there is 0.10 kg of sand in the bucket? (A) 1.5N (B) 3.5 N (C) 1.7N (D) 30 N 1

2 Rocket problem 2! A child sits in a wagon with a pile of 0.10 kg rocks. If she can throw each rock with a speed of 5 m/s relative to the ground, causing the wagon to move, how many rocks must she throw per second to maintain a constant average speed against a 3.5 N force of friction? (A) 5 rocks/second (B) 7 rocks/second (C) 10 rocks/second (D) 15 rocks/second Rotational kinematics! Just keep in mind the following table: corresponds to x corresponds to v corresponds to a For example! (constant acceleration) x = x 0 + v 0 t +1/2 a t 2 is then = t + ½ t 2 Same with other equations A student sees the following question on an exam: A flywheel with mass 120 kg, and radius 0.6 m, starting at rest, has an angular acceleration of 0.1 rad/s 2. How many revolutions has the wheel undergone after 10 s? Which formula should the student use to answer the question? A)! =! o + "t B)# = # o +! o t "t2 C)! 2 =! o 2 + 2"!# An object at rest begins to rotate with a constant angular acceleration. If this object has angular velocity ω at time t, what was its angular velocity at the time 1/2 t? A) ½ B) 1/4 C) 3/4 D) 2 E) 4 2

3 An object at rest begins to rotate with a constant angular acceleration. If this object rotates through an angle θ in the time t, through what angle did it rotate in the time 1/2 t? A) ½ B) 1/4 C) 3/4 D) 2 E) 4 Bonnie sits on the outer rim of a merry- go- round, and Klyde sits midway between the center and the rim. The merry- go- round makes one complete revolu>on every 2 seconds. Klyde s angular velocity is: a) same as Bonnie s b) twice Bonnie s c) half of Bonnie s d) one-quarter of Bonnie s e) four times Bonnie s Bonnie Klyde Rotational kinematics! BIG BEN and a little alarm clock both keep perfect time. Which minute hand has the bigger angular velocity!? A) Big Ben B) little alarm clock C) Same Rotational kinematics! For correspondence between linear and rotational terms look at the units: x = r v = r, tangential velocity a = r, tangential acceleration Centripidal acceleration: a cp = v 2 /r = r 2 2 /r = r 2 3

4 A small wheel and a large wheel are connected by a belt. The small wheel is turned at a constant angular velocity! s. There is a bug S on the rim of the small wheel and another bug L on the rim of the large wheel. How do their speeds compare? A small wheel and a large wheel are connected by a belt. The small wheel is turned at a constant angular velocity! s. How does the magnitude of the angular velocity of the large wheel! L compare to that of the small wheel?! s! L! s! L A: S = L B: S > L C: S < L A:! s =! L B:! s >! L C:! s <! L Bonnie sits on the outer rim of a merry- go- round, and Klyde sits midway between the center and the rim. The merry- go- round makes one revolu>on every 2 seconds. Who has the larger linear (tangen>al) velocity? a) Klyde b) Bonnie c) both the same d) linear velocity is zero for both of them Klyde Bonnie 4

5 A student sees the following question: An engine flywheel turns with constant angular speed of 100 rev/min. When the engine is shut off, friction slows the wheel to rest in 2 hours. What is the magnitude of the constant angular acceleration of the wheel? Give the answer in units of rev/min 2. A bike rolls to the right with speed v. What is the speed of the TOPMOST point of the front tire? A) 0 B) v C) 2v D) None of these The student writes :! =! o + "t,with! = 0,so " =! o / t " = 2# f / t " = 2# (100rev / min) /120min Does the answer come out correctly with the desired units? A) yes B) no A bike rolls to the right with speed v. What is the speed of the hub (in the middle)? A) 0 B) v C) 2v D) None of these A bike rolls to the right with speed v. What is the speed of the BOTTOM-most point (touching the ground)? A) 0 B) v C) 2v D) None of these 5

6 Suppose that the speedometer of a truck is set to read the linear speed of the truck but uses a device that actually measures the angular speed of the tires. If larger diameter tires are mounted on the truck instead, how will that affect the speedometer reading as compared to the true linear speed of the truck? a) speedometer reads a higher speed than the true linear speed b) speedometer reads a lower speed than the true linear speed c) speedometer still reads the true linear speed Reading Assignment! A bicycle coasts downhill and accelerates from rest to a linear speed of 9.0 m/s in 10 s. If the bike tires have a radius of 30 cm, what is their angular acceleration? A) 1 rad/s 2 B) 3 rad/s 2 C) 9 rad/s 2 If the tires were larger, is this number larger or smaller? Reading Assignment! Tuesday 10/ Thursday 10/