A spherically symmetric object, with radius R = 0.55 m and mass M = 1.8 kg, rolls without slipping across a horizontal floor, with velocity V = 2.6 m/s. It then rolls up an incline with an angle of inclination 0 = 27° and comes to rest a distance d = 1.5 m up the incline, before reversing direction and rolling back down. Find the moment of inertia of this object about an axis through its center of mass. d M V
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- An old grindstone, used for sharpening tools, is a solid cylindrical wheel that can rotate about its central axle with negligible friction. The radius of the wheel is 0.330 m. A constant tangential force of 300 N applied to its edge causes the wheel to have an angular acceleration of 0.848 rad/s2. (a) What is the moment of inertia of the wheel (in kg · m2)? kg · m2 (b) What is the mass (in kg) of the wheel? kg (c) The wheel starts from rest and the tangential force remains constant over a time period of 5.50 s. What is the angular speed (in rad/s) of the wheel at the end of this time period? rad/sA rotating flywheel has moment of inertia 12.0 kg ~ m2 for anaxis along the axle about which the wheel is rotating. Initially the flywheelhas 30.0 J of kinetic energy. It is slowing down with an angularacceleration of magnitude 0.500 rev/s2. How long does it take for therotational kineticenergy to become half its initial value, so it is 15.0 J?A solid horizontal cylinder rotates with an angular speed of 7.50 rad/s about a fixed vertical axis through its center. The mass of cylinder is mass 10.8 kg and its radius 1.00 m. If a piece of putty (m= 0.250-kg ) is dropped vertically onto the cylinder and sticks at a point 0.900 m from the center of rotation, what will be the final angular speed of the system.
- An airplane propeller has a mass of 72 kg and a radius of gyration of 77 cm. Find its moment of inertia. How large a torque is needed to give it an angular acceleration of 4.2 rev/s2?A skater goes for a jump with turns. When she extends her arms, her moment of inertia about an axis through his body is 1.750 kg*m2. She initially pins at 0.650 rev/s and launches herself into the air and remained there for about 1.570 seconds while spinning at a constant angular speed. Assuming that her moment of inertia about an axis through his body has a value of 0.62 kg*m2, determine how many revolutions can she execute.A solid cylinder of mass 2.7 kg and radius 0.48 m starts from rest at the top of a ramp, inclined 28°, and rolls to the bottom without slipping(For a cylinder I =; 0.5MR^2) The upper end of the ramp is 2.3 m higher than the lower end. Find the linear velocity of the cylinder when it reaches the bottom of the ramp? (g = 9.8 m/s^2)
- Conceptual Example 14 provides useful background for this problem. A playground carousel is free to rotate about its center on frictionless bearings, and air resistance is negligible. The carousel itself (without riders) has a moment of inertia of 110 kg-m2. When one person is standing at a distance of 1.71 m from the center, the carousel has an angular velocity of 0.644 rad/s. However, as this person moves inward to a point located 0.641 m from the center, the angular velocity increases to 0.832 rad/s. What is the person's mass? | | Number i UnitsAn old grindstone, used for sharpening tools, is a solid cylindrical wheel that can rotate about its central axle with negligible friction. The radius of the wheel is 0.330 m. A constant tangential force of 200 N applied to its edge causes the wheel to have an angular acceleration of 0.804 rad/s2. (a) What is the moment of inertia of the wheel (in kg · m2)? kg · m2 = (b) What is the mass (in kg) of the wheel? kg= (c) The wheel starts from rest and the tangential force remains constant over a time period of 4.50 s. What is the angular speed (in rad/s) of the wheel at the end of this time period? rad/s=A cord is wrapped around the rim of a wheel 0.300 m in radius, and a steady pull of 38.5 NN is exerted on the cord. The wheel is mounted on frictionless bearings on a horizontal shaft through its center. The moment of inertia of the wheel about this shaft is 5.35 kg⋅m2 Compute the angular acceleration of the wheel.
- A cord is wrapped around the rim of a wheel 0.225 m in radius, and a steady pull of 41.5 N is exerted on the cord. The wheel is mounted on frictionless bearings on a horizontal shaft through its center. The moment of inertia of the wheel about this shaft is 5.50 kg m² 世 ProvWe wrap a light, nonstretching cable around a solid cylinder of mass 50 kg and diameter 0.120 m, which rotates in frictionless bearings about a stationary horizontal axis. We pull the free end of the cable with a constant 9.0-N force for a distance of 2.0 m; it turns the cylinder as it unwinds without slipping. The cylinder is initially at rest. Find its final angular speed and the final speed of the cableChapter 10, Problem 057 GO A pulley, with a rotational inertia of 7.7 x 104 kg-m2 about its axle and a radius of 12 cm, is acted on by a force applied tangentiallý at its rim. The force magnitude varies in time as F = 0.80t + 0.30t, with F in newtons and t in seconds. The pulley is initially at rest. At t = 3.8 s what are (a) its angular acceleration and (b) its angular speed? (a) Number Units (b) Number Units Click if you would like to Show Work for this question: Open Show Work