Complete the table by filling in the symbols and equations. Include any notes that will help you remember and understand what these terms mean.

Transcription

1 AP Physics Rotational kinematics Rotational Kinematics Complete the table by filling in the symbols and equations. Include any notes that will help you remember and understand what these terms mean. Translational X ΔX V a Vf² Angular/Rotational Θ ΔΘ ω α ωf² Linear Kinematics Rotational Kinematics There are three linear kinematics equations on the AP 1 equation sheet, and two rotational kinematics equations. First, show how each of the three variables in a kinematics equation for linear motion corresponds to a variable for rotational/angular motion. Linear Translators Angular/Rotational angular= linear r Then, write the three linear kinematics equations and their rotational analogs. Linear Translators Angular/Rotational angular= linear r On the diagram draw and label angular velocity, linear velocity, radial/centripetal acceleration, tangential acceleration, and angular acceleration.

2 -1- n ok7ust4ad kshobfct7w9ahrmev ILwLKCE.q G oaplvlv brbizg0h4thsz mr5eisceer7vfe2dy.w b qmfa2dceu bwxibtshs yikndfvinnmihtwey SAalXg0ebbdrbaK s2a.c Worksheet by Kuta Software LLC The Unit Circle Degrees & Radians Conversion Practice Convert each degree measure into radians. 1) ) 345 3) 970 4) ) 510 ) 150 7) 210 8) ) ) 00 11) ) 75 13) ) ) ) 40 17) ) 0 19) ) 15 Convert each radian measure into degrees. 21) π 18 23) 35π 18 25) 3π 2 27) π 3 29) 11π 3 31) 14π 3 22) 25π 12 24) 41π 3 2) 107π 3 28) 17π 9 30) 41π 12 32) 1π 3

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4 Worksheet 2 Linear (translational) Kinematics 1. Use the graph to answer the following questions: (a) Give a written description of the motion of this object. (b) Calculate the average velocity from t = 0 s to t = 50 s. (c) Estimate the instantaneous velocity of the object at t = 10 s, 25 s, 38 s, 45 s. 2. Using the velocity-time graph: (a) Calculate the acceleration of the object from t = 0.5 s to t =2.5 s. (b) Calculate the displacement of the object from t = 0 s to t =2.5 s (c) Calculate the average velocity of the object from t = 0 s to t =2.5 s (d) Draw a qualitative vector diagram for the object t = 0.5 s to t = 3.0 s. Include velocity and acceleration vectors and proper labels. (e) Write a function for the velocity-time behavior of the object from t = 0.5 s to t = 2.5 s. (f) Write a function for the position-time behavior of the object from t = 0.5 s to t = 2.5 s. Include the initial position, assuming the object was at a position of x = 0 m at t = 0 s. 3

5 Angular (rotational) Kinematics 3. A particle is moving in a circle of radius 2 meters according to the relation = 3t 2 + 2t, where is measured in radians and t in seconds. The speed of the particle at t = 4 seconds is (A) 13 m/s (B) 1m/s (C) 2m/s (D) 52 m/ s (E) 338 m/ s 4. Use the theta-time graph to answer the following questions: (a) Calculate the average angular velocity of the rotating object from t = 0 s to t = 5 s. (b) Calculate the instantaneous angular velocity at t = 4 s and at t = s. (c) Describe the motion of the rotating object. 4. Use the angular velocity graph to answer the questions. (a) Calculate the average angular acceleration from t = 0 s to t = 2 s. (b) Write a function for the angular velocity versus time behavior for the interval t = 0 s to t = 2 s. (b) Calculate the angular displacement from t = 0 s to t = 4 s. (c) Write a function for the angular position of the object from t = 4 s to t = 7 s. Include the initial angular position of the object. (d) Describe the motion of the rotating object. 4

6 Worksheet 3 Angular Speed and Linear Speed A circular disk is in counterclockwise motion at a constant rate. The approximate directions of two points on the disk are shown by the arrows below. Point B Point A 1. a) Which point has the highest linear speed? b) Justify your answer: 2. a) Which point has the highest angular speed? b) Justify your answer: 3. A coin is placed on the disk at either of the two points. a)at which point would the coin be most likely to fly off? b) Justify your answer: 5

7 Custom Graph Worksheet 4 1) a-plot the following data for the wheel of an automobile. t (sec) (rad) b- What is the equation for this line? c- Determine the angular displacement in 12.5 sec for this wheel. d- What change in time starting from t = 0 sec will lead to an angular displacement of 5.00 rad? e- Plot the angular velocity as a function of time and then use the graph to determine the angular displacement from t = 1.5 s to t = 4.25 s. 2) a- Plot the following data for a wheel of a truck t (sec) (rad) b- In your own words, describe the motion of this truck wheel from t = 0 sec until t = 12s. Be sure to include the total displacement in your description. 8 Per Inch Linear Watermark MC - Port Letter

8 Custom Graph Worksheet 5 1) The following data comes from a line drawn on a wheel from the center of the wheel out to the rim. a- Plot the data. t (sec) (rad) b- What type of motion is exhibited by this graph? c- Linearize this data. d- What is the equation for the line? e- What is the angular acceleration? f- Draw a vector diagram for this extended body for the first seconds. Clearly indicate: angular position, instantaneous and linear velocities, angular velocity and angular acceleration. 2) a- A 14 inch (0.35 m) automobile tire on a car traveling at 0 mph has an angular velocity of 75.4 rad/s. If the car slows uniformly to an angular velocity of 18.7 rad/s (15 mph) in 10.0 s, what is the angular acceleration of this tire? b- What is the angular displacement of a line drawn on the tire from center point to rim during this acceleration? Give your answer in radians and in revolutions. c- What is the linear displacement the automobile during the 10.0 sec of acceleration? 8 Per Inch Linear Watermark MC - Port Letter 7

9 Custom Graph 3- A centrifuge starts from rest and reaches an angular velocity of rpm in 5.0 s. acceleration in rad/s 2 of this device? What is the angular 4- An automobile engine slows from 3000 rpm to 500 rpm in 4.0 s. engine during this time period? What is the angular displacement of the 5- A flywheel rotating at 20 rpm undergoes an angular acceleration of +2.0 rad/s 2 for precisely 5.0 revolutions. What is the angular velocity of the flywheel at the end of this acceleration? - A small rubber wheel is used to drive a large pottery wheel, and they are mounted so that their circular edges touch. If the small wheel has a radius of 3.0 cm and accelerates at the rate of 7.5 rad/s 2, and it is in contact with the pottery wheel (radius 27.0 cm) without slipping, calculate the angular acceleration of the pottery wheel, and the time it takes the pottery wheel to reach its required speed of 0 rpm. 7- The second hand of a clock makes one revolution in 0.0 sec. Draw a vector diagram for this extended body, noting the location every 10.0 sec. Indicate the angular velocity as a vector. 8- A pottery wheel has an angular velocity of 150 rpm. Convert this to rad/sec. 9- If a drill bit has an angular velocity of 377 rad/ sec. Convert this to rpm. 8 8 Per Inch Linear Watermark MC - Port Letter