Question

Starting Kinetic energy + Moment through an angle = ending kinetic energy. ? \frac{1}{2} I ?1² + ?M? = ? \frac{1}{2} I ?2² • Starting energy = 0 • Work = moment * angle (kind of like force through a distance, F dx - F r theta - M theta) • Ending energy: add together everything that is rotating • V = rw - use kinematic relationships to relate rotational velocities • I = (radius of gyration)² * mass The large gear has a mass of 4 kg and a radius of 115mm, and radius of gyration of 80 mm; The small gear has a mass of 1 kg, a radius of 55mm, and a radius of gyration of 35 mm; The system is at rest when a couple Mo of constant magnitude 3.7 N-m is applied as shown. Assuming that no slipping occurs between the gears, determine the number of revolutions of gear A required for the gear on shaft A to reach an angular velocity of 307 rpm.

          Starting Kinetic energy + Moment through an angle = ending kinetic energy.
? \frac{1}{2} I ?1² + ?M? = ? \frac{1}{2} I ?2²
• Starting energy = 0
• Work = moment * angle (kind of like force through a distance, F dx - F r theta - M theta)
• Ending energy: add together everything that is rotating
• V = rw - use kinematic relationships to relate rotational velocities
• I = (radius of gyration)² * mass
The large gear has a mass of 4 kg and a radius of 115mm, and radius of gyration of 80 mm;
The small gear has a mass of 1 kg, a radius of 55mm, and a radius of gyration of 35 mm;
The system is at rest when a couple Mo of constant magnitude 3.7 N-m is applied as shown. Assuming that no slipping occurs
between the gears, determine the number of revolutions of gear A required for the gear on shaft A to reach an angular velocity of
307 rpm.

Starting Kinetic energy + Moment through an angle = ending kinetic energy.
? (1)/(2) I ?1² + ?M? = ? (1)/(2) I ?2²
• Starting energy = 0
• Work = moment * angle (kind of like force through a distance, F dx - F r theta - M theta)
• Ending energy: add together everything that is rotating
• V = rw - use kinematic relationships to relate rotational velocities
• I = (radius of gyration)² * mass
The large gear has a mass of 4 kg and a radius of 115mm, and radius of gyration of 80 mm;
The small gear has a mass of 1 kg, a radius of 55mm, and a radius of gyration of 35 mm;
The system is at rest when a couple Mo of constant magnitude 3.7 N-m is applied as shown. Assuming that no slipping occurs
between the gears, determine the number of revolutions of gear A required for the gear on shaft A to reach an angular velocity of
307 rpm.

Added by Susan W.

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