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‫ﺗﻢ ﺗﺤﻤﻴﻞ ﻫﺬﺍ ﺍﻟﻤﻠﻒ ﻣﻦ ﻣﻮﻗﻊ ﺍﻟﻤﻨﺎﻫﺞ ﺍﻹﻣﺎﺭﺍﺗﻴﺔ‬ ‫ﻣﺮﺍﺟﻌﺔ ﻧﻬﺎﺋﻴﺔ ﻭﻓﻖ ﺍﻟﻬﻴﻜﻞ ﺍﻟﻮﺯﺍﺭﻱ ﺍﻟﺨﻄﺔ ‪C‬‬ ‫ﻣﻮﻗﻊ ﺍﻟﻤﻨﺎﻫﺞ ⇦ ﺍﻟﻤﻨﺎﻫﺞ ﺍﻹﻣﺎﺭﺍﺗﻴﺔ ⇦ ﺍﻟﺼﻒ ﺍﻟﺤﺎﺩﻱ ﻋﺸﺮ ﺍﻟﻤﺘﻘﺪﻡ ⇦ ﻓﻴﺰﻳﺎﺀ ⇦ ﺍﻟﻔﺼﻞ ﺍﻟﺜﺎﻟﺚ ⇦ ﺍﻟﻤﻠﻒ‬ ‫ﺗﺎﺭﻳﺦ ﺇﺿﺎﻓﺔ ﺍﻟﻤﻠﻒ ﻋﻠﻰ ﻣﻮﻗﻊ...

‫ﺗﻢ ﺗﺤﻤﻴﻞ ﻫﺬﺍ ﺍﻟﻤﻠﻒ ﻣﻦ ﻣﻮﻗﻊ ﺍﻟﻤﻨﺎﻫﺞ ﺍﻹﻣﺎﺭﺍﺗﻴﺔ‬ ‫ﻣﺮﺍﺟﻌﺔ ﻧﻬﺎﺋﻴﺔ ﻭﻓﻖ ﺍﻟﻬﻴﻜﻞ ﺍﻟﻮﺯﺍﺭﻱ ﺍﻟﺨﻄﺔ ‪C‬‬ ‫ﻣﻮﻗﻊ ﺍﻟﻤﻨﺎﻫﺞ ⇦ ﺍﻟﻤﻨﺎﻫﺞ ﺍﻹﻣﺎﺭﺍﺗﻴﺔ ⇦ ﺍﻟﺼﻒ ﺍﻟﺤﺎﺩﻱ ﻋﺸﺮ ﺍﻟﻤﺘﻘﺪﻡ ⇦ ﻓﻴﺰﻳﺎﺀ ⇦ ﺍﻟﻔﺼﻞ ﺍﻟﺜﺎﻟﺚ ⇦ ﺍﻟﻤﻠﻒ‬ ‫ﺗﺎﺭﻳﺦ ﺇﺿﺎﻓﺔ ﺍﻟﻤﻠﻒ ﻋﻠﻰ ﻣﻮﻗﻊ ﺍﻟﻤﻨﺎﻫﺞ‪08:17:36 2024-05-21 :‬‬ ‫ﺇﻋﺪﺍﺩ‪ :‬ﺃﺣﻤﺪ ﺍﻟﺘﻤﻴﻤﻲ‬ ‫ﺍﻟﺘﻮﺍﺻﻞ ﺍﻻﺟﺘﻤﺎﻋﻲ ﺑﺤﺴﺐ ﺍﻟﺼﻒ ﺍﻟﺤﺎﺩﻱ ﻋﺸﺮ ﺍﻟﻤﺘﻘﺪﻡ‬ ‫ﺍﺿﻐﻂ ﻫﻨﺎ ﻟﻠﺤﺼﻮﻝ ﻋﻠﻰ ﺟﻤﻴﻊ ﺭﻭﺍﺑﻂ "ﺍﻟﺼﻒ ﺍﻟﺤﺎﺩﻱ ﻋﺸﺮ ﺍﻟﻤﺘﻘﺪﻡ"‬ ‫ﺭﻭﺍﺑﻂ ﻣﻮﺍﺩ ﺍﻟﺼﻒ ﺍﻟﺤﺎﺩﻱ ﻋﺸﺮ ﺍﻟﻤﺘﻘﺪﻡ ﻋﻠﻰ ﺗﻠﻐﺮﺍﻡ‬ ‫ﺍﻟﺮﻳﺎﺿﻴﺎﺕ‬ ‫ﺍﻟﻠﻐﺔ ﺍﻻﻧﺠﻠﻴﺰﻳﺔ‬ ‫ﺍﻟﻠﻐﺔ ﺍﻟﻌﺮﺑﻴﺔ‬ ‫ﺍﻟﺘﺮﺑﻴﺔ ﺍﻻﺳﻼﻣﻴﺔ‬ ‫ﺍﻟﻤﺰﻳﺪ ﻣﻦ ﺍﻟﻤﻠﻔﺎﺕ ﺑﺤﺴﺐ ﺍﻟﺼﻒ ﺍﻟﺤﺎﺩﻱ ﻋﺸﺮ ﺍﻟﻤﺘﻘﺪﻡ ﻭﺍﻟﻤﺎﺩﺓ ﻓﻴﺰﻳﺎﺀ ﻓﻲ ﺍﻟﻔﺼﻞ ﺍﻟﺜﺎﻟﺚ‬ ‫ﺍﻟﻬﻴﻜﻞ ﺍﻟﻮﺯﺍﺭﻱ ﺍﻟﺠﺪﻳﺪ ﻣﻨﻬﺞ ﺑﺮﻳﺪﺝ ﺍﻟﺨﻄﺔ ‪ M-101-A‬ﺍﻟﻤﺴﺎﺭ‬ ‫‪1‬‬ ‫ﺍﻟﻤﺘﻘﺪﻡ‬ ‫ﺍﻟﻬﻴﻜﻞ ﺍﻟﻮﺯﺍﺭﻱ ﺍﻟﺠﺪﻳﺪ ﻣﻨﻬﺞ ﺑﺮﻳﺪﺝ ﺍﻟﺨﻄﺔ ‪ M-101-B‬ﺍﻟﻤﺴﺎﺭ‬ ‫‪2‬‬ ‫ﺍﻟﻤﺘﻘﺪﻡ‬ ‫ﺍﻟﻬﻴﻜﻞ ﺍﻟﻮﺯﺍﺭﻱ ﺍﻟﺠﺪﻳﺪ ﻣﻨﻬﺞ ﺑﺮﻳﺪﺝ ﺍﻟﺨﻄﺔ ‪ 101-C‬ﺍﻟﻤﺴﺎﺭ ﺍﻟﻤﺘﻘﺪﻡ‬ ‫‪3‬‬ ‫ﻣﺮﺍﺟﻌﺔ ﻧﻬﺎﺋﻴﺔ ﺍﺧﺘﻴﺎﺭ ﻣﻦ ﻣﺘﻌﺪﺩ ﻣﻊ ﺑﻌﺾ ﺍﻹﺟﺎﺑﺎﺕ ﻣﻨﻬﺞ ﺍﻧﺴﺒﺎﻳﺮ‬ ‫‪4‬‬  ‫ﺍﻟﻤﺰﻳﺪ ﻣﻦ ﺍﻟﻤﻠﻔﺎﺕ ﺑﺤﺴﺐ ﺍﻟﺼﻒ ﺍﻟﺤﺎﺩﻱ ﻋﺸﺮ ﺍﻟﻤﺘﻘﺪﻡ ﻭﺍﻟﻤﺎﺩﺓ ﻓﻴﺰﻳﺎﺀ ﻓﻲ ﺍﻟﻔﺼﻞ ﺍﻟﺜﺎﻟﺚ‬ ‫ﻣﻠﺨﺺ ﺍﻟﻮﺣﺪﺓ ﺍﻟﺘﺎﺳﻌﺔ ﺍﻟﺤﺮﻛﺔ ﺍﻟﺪﺍﺋﺮﻳﺔ‬ ‫‪5‬‬ ‫)‪Powered by TCPDF (www.tcpdf.org‬‬  Grade 11 Advanced (Plan C) – EoT Coverage (1) Define the center of mass as the point at which all the mass of an object appears to be Student Book MCQ 1 concentrated. (S.B) 226 (2) Recall that center of gravity is equivalent to center of mass in situations where the gravitational force is constant everywhere throughout the object. Question 1 Which of the following statements are true about the center of mass? The center of mass is always the same as the An object can have more than one center of A B center of gravity, no matter the size of the object. mass. The center of mass is where the mass of an C Some objects do not have a center of mass. D object can be considered to be concentrated. Question 2 Under which condition is the center of gravity equivalent to the center of mass for an object? When the gravitational force is constant A When the object is in motion B everywhere throughout the object C When the object is in a vacuum D When the object has uniform density Student Describe that the location of the center of mass is a fixed point relative to Book (S.B) MCQ 2 the object or system of objects and does not depend on the location of the Figure 8.2 227 coordinate system used to describe it. Concept Check 8.1 Question 3 Based on the system shown in the figure, which mass is greater than the other? What does R represent? 𝑚1 < 𝑚2 , R represents the location of the center 𝑚1 > 𝑚2 , R represents the location of the center A B of mass of the system of mass of the system 𝑚1 > 𝑚2 , R represents the location of the 𝑚1 < 𝑚2 , R represents the location of the C D geometric center of the system geometric center of the system 1 Question 4 A baseball bat has a uniform density. Which image shows a red dot at the closest point to the bat’s center of mass? A B C D Question 5 A donut-shaped object has uniform density. Which image shows a red dot at the object’s center of mass? A B C D Question 6 A system has multiple objects. Where is the center of mass of the system found? It is found at multiple points that model the It is found at multiple points that are the centers A B motion of objects in the system of mass of the objects in the system It is found at a single point at the geometric center It is found at a single point where the mass of all C D of the volume of the system the objects is concentrated Question 7 How is the mass density of an object such that the center of mass of the object is not located at the geometrical center of the body? A It will be non-homogenous B It will be constant C It will be small D It will be large 1  𝒙𝟏 𝒎 𝟏 + 𝒙𝟐 𝒎𝟐 + 𝒙𝟑 𝒎𝟑 + ⋯ 𝒚𝟏 𝒎 𝟏 + 𝒚𝟐 𝒎 𝟐 + 𝒚𝟑 𝒎 𝟑 + ⋯ 𝒛𝟏 𝒎𝟏 + 𝒛𝟐 𝒎𝟐 + 𝒛 𝟑 𝒎𝟑 + ⋯ 𝑿= 𝒀= 𝒁= 𝒎𝟏 + 𝒎𝟐 + 𝒎𝟑 + ⋯ 𝒎𝟏 + 𝒎 𝟐 + 𝒎𝟑 + ⋯ 𝒎𝟏 + 𝒎𝟐 + 𝒎 𝟑 + ⋯ Question 8 A 4.0 m rod of negligible mass connects two small spheres at its ends. The mass of one sphere is 3.0 kg and the mass of the other is unknown. What is the unknown mass if the center of mass of this system is 1.4 m to the right of the 3.0 kg sphere as shown in the figure below? A 4.2 kg B 3.4 kg C 2.7 kg D 1.6 kg Question 9 A system consists of 2 kg objects located at coordinates (0,2), (0,0), (2,0), as shown in the figure. What are coordinates (X,Y) of the center of the mass of the system? A (0.5, 0.5) B (0.67, 0.67) C (0.75, 0.75) D (1, 1) (1) Define the polar coordinate system as a two-dimensional coordinate 255 Student system such that a point on a plane is defined by its distance r from the Book (S.B) origin and the angle θ measured. S.B/Figure 256 MCQ 3 9.3/9.4 (2) Express the Cartesian coordinates (x, y) in terms of the polar coordinates (r, θ) and vice versa. Example 9.1 (3) Convert polar coordinates to Cartesian coordinates and vice versa. 256 1  Cartesian → Polar Polar → Cartesian 𝑦 𝑟= 𝑥2 + 𝑦2 𝜃 = tan−1 ( ) 𝑥 = 𝑟 𝑐𝑜𝑠 𝜃 𝑦 = 𝑟 sin(𝜃) 𝑥 Question 10 𝜋 A point has a value of (6, ) in the polar coordinate system. What is the value in cartesian coordinate? 6 A (5.0, 4.0) B (0.87, 0.50) C (4.0, 2.0) D (5.2, 3.0) Question 11 4𝜋 A point has a value of (8, 3 ) in the polar coordinate system. What is the value in cartesian coordinate? A (-7.98, -0.58) B (7.98, 0.58) C (-4.0, -6.93) D (4.0, -6.93) 1 Question 12 The cartesian coordinates of a point in the 𝑥𝑦-plane are (𝑥,𝑦)=(−3.50 𝑚,−2.50 𝑚) as shown. Find the polar coordinates of this point. A (4.30m, 216o) B (4.30m, 36o) C (2.45m, 216o) D (2.45m, 36o) Question 13 How many degrees correspond to a radian? A 57.3˚ B 90.0˚ C 180˚ D 360˚ S.B/Figure 255 Relate the arc length (s), to the radius (r) of the circular path and the angle 9.3 MCQ 4 Student (θ), measured in radians. Book 257 Question 14 A bicycle travels 141 m along a circular track of radius 30 m. What is the angular displacement in radians of the bicycle from its starting position? A 1.0 rad B 1.5 rad C 3.0 rad D 4.7 rad 1 Question 15 The track on a compact disc (CD) shown in figure. The track is a spiral, originating at an inner radius of r1 = 25 mm and terminating at an outer radius of r2 = 58 mm. The spacing between successive loops of the track is a constant, Δr = 1.6 μm. What is the total length of this track? Question 16 A child, riding on a large merry-go-round, travels a distance of 3000 m in a circle of diameter 40 m. The total angle through which she revolves is _____. A 50 rad B 75 rad C 150 rad D 314 rad Question 17 An object rotates along a circular path with a constant speed to complete 2 revolutions in 20 seconds. If the radius of this circular path is known to be 10 cm. Find the length of the path covered by the object. A 3.14m B 0.58m C 1.26m D 4.3m Question 18 A drone flies along a circular path and completes 3 revolutions in 15 minutes. If the length of the path covered by the drone is 1.5 kilometers, what is the diameter of the circular path? A 80m B 160m C 320m D 540m 1  Example 9.3 260 Apply the relation for the magnitude of angular velocity in terms of MCQ 5 Additional frequency and period of rotation Exercises/9.61(a) 282 𝟐𝝅 𝝎 = 𝟐𝝅𝒇 = 𝐓 𝒗 = 𝒓𝝎 Question 19 The Earth orbits around the Sun and also rotates on its pole-to-pole axis. What are the angular velocities, frequencies, and linear speeds of these motions? Question 20 A boy is on a Ferris wheel, which takes him in a vertical circle of radius 9.00 m once every 12.0 s. What is the angular speed of the Ferris wheel? 1 Question 21 The angular speed of the minute hand of a clock (in radians per second) is: A 0.05 rad/s B 6.28 rad/s C 3.20 rad/s D 0.10 rad/s Relate the magnitudes of linear (tangential) and angular velocities for Exercises/Q. MCQ 6 circular motion as, and explain that this relation does not hold for 281 9.44 tangential and angular velocity vectors which point in different directions 𝒗 = 𝒓𝝎 Question 22 The figure shows a cylinder of radius 0.7 m rotating about its axis at 10 rad/s. The linear speed of the point P is: A 4.0 m/s B 7.0 m/s C 11.0 m/s D 13.0 m/s Question 23 A car travels along a circular track and completes 4 revolutions in 40 seconds. If the radius of this circular track is 20 meters, calculate the angular velocity and the linear velocity of the car at the time it completes the 4 revolutions. A 0.43 rad/s - 12.57 m/s B 0.63 rad/s – 6.58 m/s C 0.63 rad/s - 12.57 m/s D 0.84 rad/s - 12.57 m/s 1  Exercises for Question 9.44 (part f), 281 Relate the magnitude of the net acceleration in circular motion to the Exercises for MCQ 7 Question 9.46, tangential acceleration and centripetal acceleration Additional 282 Exercises for Question 9.63. 262 Express the linear acceleration vector for an object in circular motion as (S.B) MCQ 13 𝑎⃑ = 𝑎𝑡 𝑡̂ − 𝑎𝑐 𝑟̂ Exercise/Q.9.46 281 ⃑⃑ = 𝒂𝒕 𝒕̂ − 𝒂𝒄 𝒓̂ 𝒂 𝒂𝒕 = 𝒓𝜶 𝒗𝟐𝟐 𝒂𝒄 = 𝒗𝝎 = 𝝎 𝒓 = 𝒓 Question 24 A discus thrower (with arm length of 1.20 m) starts from rest and begins to rotate counterclockwise with an angular acceleration of 2.50 rad/s2. a) How long does it take the discus thrower’s speed to get to 4.70 rad/s? b) How many revolutions does the thrower make to reach the speed of 4.70 rad/s? c) What is the linear speed of the discus at 4.70 rad/s? d) What is the linear acceleration of the discus thrower at this point? e) What is the magnitude of the centripetal acceleration of the discus thrown? f) What is the magnitude of the discus’s total acceleration? 1 Question 25 A particle is moving clockwise in a circle of radius 1.00 m. At a certain instant, the magnitude of its acceleration is a = 25.0 m/s2 and the acceleration vector has an angle of θ = 50.0° with the position vector, as shown in the figure. At ⃑⃑⃑ of this particle. this instant, find the speed, 𝑣 = |𝑣| Question 26 A car accelerates uniformly from rest and reaches a speed of 22.0 m/s in 9.00 s. The diameter of a tire on this car is 58.0 cm. a) Find the number of revolutions the tire makes during the car’s motion, assuming that no slipping occurs. b) What is the final angular speed of a tire in revolutions per second? 1  Identify that the centripetal force, necessary for circular motion, can be Student Book 264 (S.B) MCQ 8 provided by different forces such as the force of friction, tension, Exercises/Q. gravitational force, Coulomb force, or the normal force. 9.50 281 𝒗𝟐 𝑭𝒄 = 𝒎𝒂𝒄 = 𝒎𝒗𝝎 = 𝒎 = 𝒎𝝎𝟐 𝒓 𝒓 Question 27 Calculate the centripetal force exerted on a vehicle of mass m = 1500. kg that is moving at a speed of 15.0 m/s around a curve of radius R = 400. m. Which force plays the role of the centripetal force in this case? Question 28 Calculate the centripetal force exerted on a stone of mass 𝑚 = 2.0 kg that is being swung at a speed of 6.0 m/s around a circular path with a radius R=1.5 meters. Which force plays the role of the centripetal force in this case? 1  Apply the kinematic relationships for circular motion with constant angular Example 9.6 264 Example 9.7 MCQ 9 acceleration to calculate angular position, angular displacement, angular Exercises/Q. 271 velocity, angular acceleration, or time. 9.35 280 Question 29 In Example 9.2, we established that a CD track is 5.4 km long. A music CD can store 74 min of music. What are the angular velocity and the tangential acceleration of the disc as it spins inside a CD player, assuming a constant linear velocity? Question 30 In hammer throw competetion, the hammer’s total length is 121.5 cm, and its total mass is 7.26 kg. The athlete has to accomplish the throw from within a circle of radius 2.13 m, and the best way to throw the hammer is for the athlete to spin, allowing the hammer to move in a circle around him, before releasing it. An athlete broke the Olympic record distance of 84.80 m. He took seven turns before releasing the hammer, and the period to complete each turn was obtained from examining the video recording frame by frame: 1.52 s, 1.08 s, 0.72 s, 0.56 s, 0.44 s, 0.40 s, and 0.36 s. a) What was the average angular acceleration during the seven turns? Assume constant angular acceleration for the solution. 1  b) Assuming that the radius of the circle on which the hammer moves is 1.67 m (the length of the hammer plus the arms of the athlete), what is the linear speed with which the hammer is released? c) What is the centripetal force that the hammer thrower has to exert on the hammer right before he releases it? d) After release, what is the direction in which the hammer moves? Question 31 A vinyl record plays at 33.3 rpm. Assume it takes 5.00 s for it to reach this full speed, starting from rest. a) What is its angular acceleration during the 5.00 s? b) How many revolutions does the record make before reaching its final angular speed? 1  Student MCQ 10 Convert angle measurements between degrees and radians. Book (S.B) 256 Question 32 One complete revolution (360˚) is the same as 𝝅 𝝅 A 𝒓𝒂𝒅 B 𝒓𝒂𝒅 𝟒 𝟐 C 𝝅 𝒓𝒂𝒅 D 𝟐𝝅 𝒓𝒂𝒅 Question 33 1. Convert 3 revolution into degrees. 4 2. Convert (3 𝜋) 𝑟𝑎𝑑 to revolutions. 3. Convert 225o to revolutions. 1  Sketch the path taken in circular motion (uniform and non-uniform) and S.B/Figure 262 MCQ 11 explain the velocity and acceleration vectors (magnitudes and directions) 9.12 during the motion S.B/MCQ/Q.9.4 278 Question 34 A rock attached to a string moves clockwise in uniform circular motion. In which direction from point A is the rock thrown off when the string is cut? A (a) B (b) C (c) D (d) Question 35 Consider an object that moves in a circular path at constant speed. When it reaches point A, which of the following describes the direction of its centripetal acceleration (𝑎c) and velocity (𝑣)? A ac v B ac v C ac v D ac v 1  Identify that for an object in circular motion with a given angular velocity, (S.B) 264 MCQ 12 Example 9.8 the centripetal force increases with the distance from the center. 273 𝟒𝝅𝟐 𝒓 𝑭𝒄 = 𝒎 ∙ 𝟐 𝑻 Question 36 Which piece would fall first as the angular speed of the spinning table increases? A (a) B (b) C (c) D (d) Question 37 Suppose that cars move through the U-turn shown in Figure at constant speed and that the coefficient of static friction between the tires and the road is μs = 1.2. If the radius of the inner curve shown in the figure is RB = 10.3 m and radius of the outer is RA = 32.2 m and the cars move at their maximum speed, how much time will it take to move from point A to A' and from point B to B'? 1  Student 261 Distinguish between tangential acceleration and radial acceleration, Book (S.B) MCQ 14 Exercises/ specifying the cause and direction of each. Q. 9.46/9.43 281 Question 38 Calculate the required frequency and the linear speed of a sample in an ultracentrifuge. The sample is subjected to a centripetal acceleration of 840,000 𝑔 at a distance of 23.5 cm from the ultracentrifuge’s rotation axis. Question 39 A centrifuge in a medical laboratory rotates at an angular speed of 3600. rpm (revolutions per minute). When switched off, it rotates 60.0 times before coming to rest. Find the constant angular acceleration of the centrifuge. 1  Apply Newton’s laws of motion and/or energy conservation principles to S.B/Figure 9.18/9.19 266 analyze circular motion in a vertical or horizontal plane (motion in vertical MCQ 15 S.B/Figure 9.20 268 loop of an amusement park ride, rotating cylinder, moving through a S.B/MCQ/Q.9.11 278 levelled or banked curve,... ) Added Q Question 40 Perhaps the biggest thrill to be had at an amusement park is on a roller coaster with a vertical loop in it , where passengers feel almost weightless at the top of the loop. Suppose the vertical loop has a radius of 5.00 m. What does the linear speed of the roller coaster have to be at the top of the loop for the passengers to feel weightless? (Assume that friction between roller coaster and rails can be neglected.) What speed must the roller coaster have at the top of the loop to accomplish the same feeling of weightlessness if the radius of the loop is doubled? Question 41 One of the rides found at carnivals is a rotating cylinder. The riders step inside the vertical cylinder and stand with their backs against the curved wall. The cylinder spins very rapidly, and at some angular velocity, the floor is pulled away. The thrill-seekers now hang like flies on the wall. If the radius of the cylinder is r = 2.10 m, the rotation axis of the cylinder remains vertical, and the coefficient of static friction between the people and the wall is μs = 0.390, what is the minimum angular velocity, ω, at which the floor can be withdrawn? 1 Question 42 The figure shows a rider stuck to the wall without touching the floor in the Barrel of Fun at a carnival. Which diagram correctly shows the forces acting on the rider? Question 43 An amusement park ride has the shape of a cylindrical shell of radius 12 m. First, a passenger stands against the wall of the ride, and when the ride reaches a speed of 15 m/s, the floor underneath the passenger is lowered. What is the minimum coefficient of static friction that allows the passenger to remain pinned against the wall of the ride? A 0.52 B 0.68 C 0.71 D 0.80 End of MCQ part 1  (1) Identify that the linear velocity, of a particle in circular motion always points tangential to the circular path (circumference) and is always perpendicular to the position vector, which points in the radial direction. (2) Sketch the path taken in circular motion (uniform and non-uniform) and Exercises/Q. explain the velocity and acceleration vectors (magnitudes and directions) 9.46 Exercises/Q. FRQ 16 during the motion. 9.47.(a) 281 (3) Explain that for uniform circular motion, where the angular velocity is Exercises/Q. constant, the tangential acceleration is zero, but the velocity vector still 9.50 changes direction continuously as the object moves in its circular path. (4) Relate the magnitudes of linear (tangential) and angular velocities for circular motion. Question 44 In a tape recorder, the magnetic tape moves at a constant linear speed of 5.60 cm/s. To maintain this constant linear speed, the angular speed of the driving spool (the take-up spool) has to change accordingly. a) What is the angular speed of the take-up spool when it is empty, with radius r1 = 0.800 cm? b) What is the angular speed when the spool is full, with radius r2 = 2.20 cm? c) If the total length of the tape is 100.80 m, what is the average angular acceleration of the take-up spool while the tape is being played? 1  Solved (1) Apply Newton’s laws of motion and/or energy conservation principles to Problem analyze circular motion in a vertical or horizontal plane (motion in vertical (9.1) loop of an amusement park ride, rotating cylinder, moving through a Conceptual 266 levelled or banked curve... ). Questions 279 FRQ 17 (9.20) (2) Determine the location of the center of mass of two or several particles Exercises/Q. 281 or extended objects with uniform mass distribution (the object can be 9.55 282 divided into simple geometric figures, each of which can be replaced by a Additional particle at its center) by applying suitable mathematical equations Exercises/Q. 9.60 𝑬 = 𝑲+𝑼 Question 45 ‫) في االعلى‬40( ‫تابع لسؤال‬ Find the velocities at 3 o’clock and 9 o'clock positions. What is the apparent weight of a rider on the roller coaster at the bottom of the loop? 1 Question 46 A person rides on a Ferris wheel of radius R, which is rotating at a constant angular velocity ω. Compare the normal force of the seat pushing up on the person at point A to that at point B in the figure. Which force is greater, or are they the same? Question 47 A particular Ferris wheel takes riders in a vertical circle of radius 9.00 m once every 12.0 s. a) Calculate the speed of the riders, assuming it to be constant. b) Draw a free-body diagram for a rider at a time when she is at the bottom of the circle. Calculate the normal force exerted by the seat on the rider at that point in the ride. c) Perform the same analysis as in part (b) for a point at the top of the ride. 1 Question 48 Given a banked curve with a radius of 𝑅=110m and a banking angle of 𝜃=21.1∘, calculate the maximum speed a driver can maintain without slipping if the coefficient of static friction between the track and the tires is 𝜇𝑠=0.620. Find the minimum speed at which the car can travel with as it negotiates the banked curve? 1  Find the minimum speed at which the car has to move with if the surface is frictionless. Question 49 A car speeds over the top of a hill. If the radius of curvature of the hill at the top is 9.00 m, how fast can the car be traveling and maintain constant contact with the ground? (1) Apply the kinematic relationships for circular motion with constant Exercises/Q. angular acceleration to calculate angular position, angular displacement, 9.35 Exercises/Q. 280 angular velocity, angular acceleration, or time. FRQ 18 9.44 281 (2) Solve problems related to rotation with constant angular acceleration. Additional (3) Relate the magnitude of the net acceleration in circular motion to the 282 Exercises/Q. tangential acceleration and centripetal acceleration. 9.63 All questions mentioned in this part were solved in the previous parts. (Repeated questions) Apply Newton’s laws of motion and/or energy conservation principles to Solved analyze circular motion in a vertical or horizontal plane (motion in vertical Problem 275 FRQ 19 /Q.9.4 loop of an amusement park ride, rotating cylinder, moving through a Exercises/Q. 282 levelled or banked curve... ). 9.59 1 Question 50 A speedway turn, with radius of curvature R, is banked at an angle 𝜃 above the horizontal. a) What is the optimal speed at which to take the turn if the track’s surface is iced over (that is, if there is very little friction between the tires and the track)? b) If the track surface is ice-free and there is a coefficient of friction μs between the tires and the track, what are the maximum and minimum speeds at which this turn can be taken? c) Evaluate the results of parts (a) and (b) for R = 400. m, 𝜃 = 45.0°, and μs = 0.700. Question 51 The raceway of a car race is banked at an angle 𝜃 above the horizontal. What must the value of 𝜃 be if a race car, moving with a speed of 45 m/s, maintains a circular motion of radius 320 m, assuming it is raining and the friction between the tires and the road is negligible? End of FRQ part ‫مع تم نايتي لكم بال توف تق والنجاح‬ 1