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80, ential and components of a discus as it is being thrown. A discus thrower turns with angular acceleration a = 50rad/s², moving the discus in a circle of radius 0.80 m (Figure 1). Find the radial and tangential components of acceleration of the discus (modeled as a point) and the magnitude of its acceleration at the instant when the angular velocity is 10 rad/s. Figure Ar arad 1 of 2 > the discus as a particle moving in a circular path. SOLVE The components of the acceleration are given by arad = = atan The magnitude of the acceleration vector is a = √arad²+atan² = 89 m/s² REFLECT The magnitude of the acceleration is about nine times the acceleration due to gravity; the corresponding force supplied by the thrower's arm must be about nine times the weight of the discus. Note that we have omitted the unit radian in our final results; we can do th because a radian is a dimensionless quantity. Part A - Practice Problem: w²r= (10rad/s)² (0.80m) = 80 m/s² ra = (0.80m) (50rad/s²) = 40 m/s² What is the direction of the acceleration vector of the discus if the angular acceleration is 37 rad/s² and w = 10.0? Express your answer in degrees to two significant figures. Measure the angle from the radial line between the center of the discus and the thrower's shoulder. | ΑΣΦ www. ?

80, ential and components of a discus as it is being thrown. A discus thrower turns with angular acceleration a = 50rad/s², moving the discus in a circle of radius 0.80 m (Figure 1). Find the radial and tangential components of acceleration of the discus (modeled as a point) and the magnitude of its acceleration at the instant when the angular velocity is 10 rad/s. Figure Ar arad 1 of 2 > the discus as a particle moving in a circular path. SOLVE The components of the acceleration are given by arad = = atan The magnitude of the acceleration vector is a = √arad²+atan² = 89 m/s² REFLECT The magnitude of the acceleration is about nine times the acceleration due to gravity; the corresponding force supplied by the thrower's arm must be about nine times the weight of the discus. Note that we have omitted the unit radian in our final results; we can do th because a radian is a dimensionless quantity. Part A - Practice Problem: w²r= (10rad/s)² (0.80m) = 80 m/s² ra = (0.80m) (50rad/s²) = 40 m/s² What is the direction of the acceleration vector of the discus if the angular acceleration is 37 rad/s² and w = 10.0? Express your answer in degrees to two significant figures. Measure the angle from the radial line between the center of the discus and the thrower's shoulder. | ΑΣΦ www. ?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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80, 29.6, Now let's consider the tangential and radial components of a discus as it is being thrown. A discus thrower turns with angular acceleration a = 50rad/s², moving the discus in a circle of radius 0.80 m (Figure 1). Find the radial and tangential components of acceleration of the discus (modeled as a point) and the magnitude of its acceleration at the instant when the angular velocity is 10 rad/s. Figure atan arad 1 of 2 > SOLUTION SET UP As shown in (Figure 2), we model the thrower's arm as a rigid body, so r is constant (this may not be completely realistic). We model the discus as a particle moving in a circular path. SOLVE The components of the acceleration are given by The magnitude of the acceleration vector is Part A Practice Problem: arad atan - ΑΣΦ w²r= (10rad/s)² (0.80m) = 80 m/s² ra = (0.80m) (50rad/s²) = 40 m/s² a = REFLECT The magnitude of the acceleration is about nine times the acceleration due to gravity; the corresponding force supplied by the thrower's arm must be about nine times the weight of the discus. Note that we have omitted the unit radian in our final results; we can do this because a radian is a dimensionless quantity. 2 arad²+atan = 89 m/s² What is the direction of the acceleration vector of the discus if the angular acceleration is 37 rad/s² and w = 10.0? Express your answer in degrees to two significant figures. Measure the angle from the radial line between the center of the discus and the thrower's shoulder. ?
Transcribed Image Text:80, 29.6, Now let's consider the tangential and radial components of a discus as it is being thrown. A discus thrower turns with angular acceleration a = 50rad/s², moving the discus in a circle of radius 0.80 m (Figure 1). Find the radial and tangential components of acceleration of the discus (modeled as a point) and the magnitude of its acceleration at the instant when the angular velocity is 10 rad/s. Figure atan arad 1 of 2 > SOLUTION SET UP As shown in (Figure 2), we model the thrower's arm as a rigid body, so r is constant (this may not be completely realistic). We model the discus as a particle moving in a circular path. SOLVE The components of the acceleration are given by The magnitude of the acceleration vector is Part A Practice Problem: arad atan - ΑΣΦ w²r= (10rad/s)² (0.80m) = 80 m/s² ra = (0.80m) (50rad/s²) = 40 m/s² a = REFLECT The magnitude of the acceleration is about nine times the acceleration due to gravity; the corresponding force supplied by the thrower's arm must be about nine times the weight of the discus. Note that we have omitted the unit radian in our final results; we can do this because a radian is a dimensionless quantity. 2 arad²+atan = 89 m/s² What is the direction of the acceleration vector of the discus if the angular acceleration is 37 rad/s² and w = 10.0? Express your answer in degrees to two significant figures. Measure the angle from the radial line between the center of the discus and the thrower's shoulder. ?
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