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At a given instant the body of mass m has an angular velocity w and its mass center has a velocity VG. Show that its kinetic energy can be represented as T = Iicw?, where Iç is the moment of inertia of the body determined about the instantaneous axis of zero velocity, located a distance rG/Ic from the mass center as shown. The wheel is made from a 5-kg thin ring and two 2-kg slender rods. If the torsional spring attached to the wheelľ's center has a stiffness k = 2 N • m/rad, so that the torque on the center of the wheel is M = (20) N•m, where 0 is in radians, determine the maximum angular velocity of the wheel if it is rotated two revolutions and then released from rest. Partial Ans. 14.1 rad/s

At a given instant the body of mass m has an angular velocity w and its mass center has a velocity VG. Show that its kinetic energy can be represented as T = Iicw?, where Iç is the moment of inertia of the body determined about the instantaneous axis of zero velocity, located a distance rG/Ic from the mass center as shown. The wheel is made from a 5-kg thin ring and two 2-kg slender rods. If the torsional spring attached to the wheelľ's center has a stiffness k = 2 N • m/rad, so that the torque on the center of the wheel is M = (20) N•m, where 0 is in radians, determine the maximum angular velocity of the wheel if it is rotated two revolutions and then released from rest. Partial Ans. 14.1 rad/s

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Work and Energy: Rigid Body 1) At a given instant the body of mass m has an angular velocity w and its mass center has a velocity vg. Show that its kinetic energy can be represented as T = Ijcw², where Iç is the moment of inertia of the body determined about the instantaneous axis of zero velocity, located a distance ľG/Ic from the mass center as shown. IC G The wheel is made from a 5-kg thin ring and two 2-kg slender rods. If the torsional spring attached to the wheel's center has a stiffness k = 2 N •m/rad, so that the torque on the center of the wheel is M = (20) N · m, where 0 is in radians, determine the maximum angular velocity of the wheel if it is 0.5 m rotated two revolutions and then released from rest. M Partial Ans. 14.1 rad/s
Transcribed Image Text:Work and Energy: Rigid Body 1) At a given instant the body of mass m has an angular velocity w and its mass center has a velocity vg. Show that its kinetic energy can be represented as T = Ijcw², where Iç is the moment of inertia of the body determined about the instantaneous axis of zero velocity, located a distance ľG/Ic from the mass center as shown. IC G The wheel is made from a 5-kg thin ring and two 2-kg slender rods. If the torsional spring attached to the wheel's center has a stiffness k = 2 N •m/rad, so that the torque on the center of the wheel is M = (20) N · m, where 0 is in radians, determine the maximum angular velocity of the wheel if it is 0.5 m rotated two revolutions and then released from rest. M Partial Ans. 14.1 rad/s
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