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Unformatted text preview: Homework Set 4 Ch 9: 32 A 12-m-radius Ferris wheel rotates once each 27 s. ( a ) What is its angular speed (in radians per second)? ( b ) What is the linear speed of a passenger? ( c ) What is the acceleration of a passenger? Picture the Problem We can find the angular speed of the Ferris wheel from its definition and the linear speed and centripetal acceleration of the passenger from the relationships between those quantities and the angular speed of the Ferris wheel. ( a ) Find from its definition: rad/s 23 . rad/s 233 . s 27 rad 2 = = = = t ( b ) Find the linear speed of the passenger from his/her angular speed: ( )( ) m/s 8 . 2 rad/s 0.233 m 12 = = = r v Find the passengers centripetal acceleration from his/her angular speed: ( )( ) 2 2 2 c m/s 65 . rad/s 0.233 m 12 = = = r a 41 [SSM] Four particles, one at each of the four corners of a square with 2.0-m long edges, are connected by massless rods (Figure 9-45). The masses of the particles are m 1 = m 3 = 3.0 kg and m 2 = m 4 = 4.0 kg. Find the moment of inertia of the system about the z axis. Picture the Problem The moment of inertia of a system of particles with respect to a given axis is the sum of the products of the mass of each particle and the square of its distance from the given axis. Use the definition of the moment of inertia of a system of four particles to obtain: 2 4 4 2 3 3 2 2 2 2 1 1 i 2 i i r m r m r m r m r m I + + + = = Substitute numerical values and evaluate I z axis : ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 axis m kg 56 kg 4.0 m 2.0 kg 3.0 m 2 2 kg 4.0 m 2.0 kg 3.0 = + + + = z I 44 Determine the moment of inertia of a uniform solid sphere of mass M and radius R about an axis that is tangent to the surface of the sphere (Figure 9-46). Picture the Problem According to the parallel-axis theorem, where I cm is the moment of inertia of the object with respect to an axis through its center of mass, M is the mass of the object, and h is the distance between the parallel axes. , 2 cm Mh I I + = The moment of inertia of a solid sphere of mass M and radius R about an axis that is tangent to the sphere is given by: 2 cm Mh I I + = (1) Use Table 9-1 to find the moment of inertia of a sphere with respect to an axis through its center of mass: 2 5 2 cm MR I = Substitute for I cm and h in equation (1) and simplify to obtain:...
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