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Learning Goal: To understand the kinetic energy of a rigid body undergoing translational motion, rotation about a fixed axis, or general motion in the plane. Consider the rigid body shown in the figure. (Figure 1) An arbitrary th particle of the body, having mass dm, is located a distance r from an arbitrary point P in the inertial z-y reference plane. If, at the instant shown, the particle has a velocity v₁, then the particle's kinetic energy is T₁ = (dm)v². The kinetic energy of the entire body is found by summing similar equations for each particle in the body. As the number of particles increases, by letting the size of each particle go to an infinitesimally small volume, the sum becomes an integral and the kinetic energy of the body is T = m dm v². Figure 2 of 3 > ▾ Part A - Kinetic Energy of a Pulley and Weight System Consider the pulley and weight system shown in the figure. (Figure 2) The pulley has mass 12.0 kg, outer radius Ro = 150 mm, inner radius R; = 100 mm, and radius of gyration ko = 123 mm. Cylinder A weighs 73.0 N. Assume there is no friction between the pulley and its axle and that the rope is massless. At the instant when w = 81.0 rad/s clockwise, what is the kinetic energy of the system? Express your answer to three significant figures and include the appropriate units. ▸ View Available Hint(s) Submit A T= Value LA T= D ← ▼ Part B - Kinetic Energy of a Rolling Bicycle Wheel HA The bicycle wheel shown in the figure rolls without slipping. (Figure 3) The wheel has a weight of 5.70 lb, a radius of r= 13.0 in, and is rolling in such a way that the center hub, O, is moving to the right at a constant speed of v= 12.0 ft/s. Assume all the mass is evenly distributed at the outer radius r of the wheel/tire assembly. What is the total kinetic energy of the bicycle wheel? Express your answer to three significant figures and include the appropriate units. View Available Hint(s) Value Units 5 PAC → ? Units Review Pa ?

Learning Goal: To understand the kinetic energy of a rigid body undergoing translational motion, rotation about a fixed axis, or general motion in the plane. Consider the rigid body shown in the figure. (Figure 1) An arbitrary th particle of the body, having mass dm, is located a distance r from an arbitrary point P in the inertial z-y reference plane. If, at the instant shown, the particle has a velocity v₁, then the particle's kinetic energy is T₁ = (dm)v². The kinetic energy of the entire body is found by summing similar equations for each particle in the body. As the number of particles increases, by letting the size of each particle go to an infinitesimally small volume, the sum becomes an integral and the kinetic energy of the body is T = m dm v². Figure 2 of 3 > ▾ Part A - Kinetic Energy of a Pulley and Weight System Consider the pulley and weight system shown in the figure. (Figure 2) The pulley has mass 12.0 kg, outer radius Ro = 150 mm, inner radius R; = 100 mm, and radius of gyration ko = 123 mm. Cylinder A weighs 73.0 N. Assume there is no friction between the pulley and its axle and that the rope is massless. At the instant when w = 81.0 rad/s clockwise, what is the kinetic energy of the system? Express your answer to three significant figures and include the appropriate units. ▸ View Available Hint(s) Submit A T= Value LA T= D ← ▼ Part B - Kinetic Energy of a Rolling Bicycle Wheel HA The bicycle wheel shown in the figure rolls without slipping. (Figure 3) The wheel has a weight of 5.70 lb, a radius of r= 13.0 in, and is rolling in such a way that the center hub, O, is moving to the right at a constant speed of v= 12.0 ft/s. Assume all the mass is evenly distributed at the outer radius r of the wheel/tire assembly. What is the total kinetic energy of the bicycle wheel? Express your answer to three significant figures and include the appropriate units. View Available Hint(s) Value Units 5 PAC → ? Units Review Pa ?

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Learning Goal: To understand the kinetic energy of a rigid body undergoing translational motion, rotation about a fixed axis, or general motion in the plane. Consider the rigid body shown in the figure. (Figure 1) An arbitrary th particle of the body, having mass dm, is located a distance r from an arbitrary point P in the inertial x-y reference plane. If, at the instant shown, the particle has a velocity vi, then the particle's kinetic energy is T₁ = 1/(dm) v². The kinetic energy of the entire body is found by summing similar equations for each particle in the body. As the number of particles increases, by letting the size of each particle go to an infinitesimally small volume, the sum becomes an integral and the kinetic energy of the body is T = 1/2 √m dm v ². Figure (1) R₁ A Ro < 2 of 3 Part A Kinetic Energy of a Pulley and Weight System Consider the pulley and weight system shown in the figure. (Figure 2) The pulley has mass 12.0 kg, outer radius Ro= 150 mm, inner radius Ri = 100 mm, and radius of gyration ko = 123 mm. Cylinder A weighs 73.0 N. Assume there is no friction between the pulley and its axle and that the rope is massless. At the instant when w = 81.0 rad/s clockwise, what is the kinetic energy of the system? Express your answer to three significant figures and include the appropriate units. View Available Hint(s) T= Submit 0 μà Value Units Part B - Kinetic Energy of a Rolling Bicycle Wheel μA ? The bicycle wheel shown in the figure rolls without slipping. (Figure 3) 12.0 ft/s. The wheel has a weight of 5.70 lb, a radius of r = 13.0 in, and is rolling in such a way that the center hub, O, is moving to the right at a constant speed of v = Assume all the mass is evenly distributed at the outer radius r of the wheel/tire assembly. What is the total kinetic energy of the bicycle wheel? Express your answer to three significant figures and include the appropriate units. ► View Available Hint(s) T = Value Units Review ?
Transcribed Image Text:Learning Goal: To understand the kinetic energy of a rigid body undergoing translational motion, rotation about a fixed axis, or general motion in the plane. Consider the rigid body shown in the figure. (Figure 1) An arbitrary th particle of the body, having mass dm, is located a distance r from an arbitrary point P in the inertial x-y reference plane. If, at the instant shown, the particle has a velocity vi, then the particle's kinetic energy is T₁ = 1/(dm) v². The kinetic energy of the entire body is found by summing similar equations for each particle in the body. As the number of particles increases, by letting the size of each particle go to an infinitesimally small volume, the sum becomes an integral and the kinetic energy of the body is T = 1/2 √m dm v ². Figure (1) R₁ A Ro < 2 of 3 Part A Kinetic Energy of a Pulley and Weight System Consider the pulley and weight system shown in the figure. (Figure 2) The pulley has mass 12.0 kg, outer radius Ro= 150 mm, inner radius Ri = 100 mm, and radius of gyration ko = 123 mm. Cylinder A weighs 73.0 N. Assume there is no friction between the pulley and its axle and that the rope is massless. At the instant when w = 81.0 rad/s clockwise, what is the kinetic energy of the system? Express your answer to three significant figures and include the appropriate units. View Available Hint(s) T= Submit 0 μà Value Units Part B - Kinetic Energy of a Rolling Bicycle Wheel μA ? The bicycle wheel shown in the figure rolls without slipping. (Figure 3) 12.0 ft/s. The wheel has a weight of 5.70 lb, a radius of r = 13.0 in, and is rolling in such a way that the center hub, O, is moving to the right at a constant speed of v = Assume all the mass is evenly distributed at the outer radius r of the wheel/tire assembly. What is the total kinetic energy of the bicycle wheel? Express your answer to three significant figures and include the appropriate units. ► View Available Hint(s) T = Value Units Review ?
Figure < Vo 3 of 3 The bicycle wheel shown in the figure rolls without slipping. (Figure 3) The wheel has a weight of 5.70 lb, a radius of r = 13.0 in, and is rolling in such a way that the center hub, O, is moving to the right at a constant speed of v = = 12.0 ft/s. Assume all the mass is evenly distributed at the outer radius r of the wheel/tire assembly. What is the total kinetic energy of the bicycle wheel? Express your answer to three significant figures and include the appropriate units. ► View Available Hint(s) T = μĂ Value Units ?
Transcribed Image Text:Figure < Vo 3 of 3 The bicycle wheel shown in the figure rolls without slipping. (Figure 3) The wheel has a weight of 5.70 lb, a radius of r = 13.0 in, and is rolling in such a way that the center hub, O, is moving to the right at a constant speed of v = = 12.0 ft/s. Assume all the mass is evenly distributed at the outer radius r of the wheel/tire assembly. What is the total kinetic energy of the bicycle wheel? Express your answer to three significant figures and include the appropriate units. ► View Available Hint(s) T = μĂ Value Units ?
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