consists of four boxes modeled as particles connected by very lightweight, stiff rods (see figure below). The system rotates around the z axis, which points out of the page. Each particle has a mass of 7.00 kg. The distances from the z axis to each particle are r1 = 48.0 cm, r2 = 24.0 cm, r3 = 19.0 cm, and r4 = 38.0 cm. Find the rotational

Determine the speed of the block with a mass of 0.60 kg after it has fallen 145 cm. The sphere is a shell with M = 4.5 kg and R = 8.5 cm. The pully has a rotational inertia of 0.0030 kg m2 and r = 5.0 cm. Use g = 9.8 m/s/s. Use conservation of energy.

Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel's energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 1.5 m diameter and a mass of 250 kg. A motor spins up the flywheel with a constant torque of 50N⋅m50N⋅m. How long does it take the flywheel to reach top angular speed of 1200 rpm?   Show a diagram

The figure above shows two barbells, which can be modeled as two point masses connected by a massless rod. In the figure, L = 0.77 m and m = 20.1 kg. The barbells can rotate about an axis that is perpendicular to the rod and passes through the midpoint of each rod. For the barbell with the larger moment of inertia, give the moment of inertia (in units of kg m2).

A mass (M = 5.0 kg) is connected to a two pulley system. Pulley 1 has a moment of inertia, I = 0.5 kgm2, and a radius, R = 0.2 m. Pulley 2 has moment of inertia, I = 0.3 kgm2, and a radius, R = 0.15 m. The cord is spooled around pulley 2. The pulleys rotate about frictionless axles and the cord can be considered massless. (i) Determine the magnitude of the acceleration of m (ii) Determine the magnitude of the tension in the string attached to m (iii) Determine the magnitude of the tension between the pulleys.

Wile E. Coyote wants to flatten the Road Runner. Wile E. puts food at a pre-determined distance from the edge of a cliff. While the Road Runner eats the food, Wile E. pushes a log down the hill. It rolls without slipping. The radius of the log is 0.3 m. The mass of the log is 80 kg. The rotational inertia of the log is given by I = ½ MR2 . The translational speed of the log just before it leaves the cliff horizontally is 16 m/s. The Road Runner is 10 m below the cliff. If the log is to successfully hit the Road Runner, the food must be place at a precise location from the base of the cliff which you will determine. a. Use only energy considerations and the fact that the log does not slip as it rolls to determine the height it started from, h, before it went over the cliff. b. Determine how far from the edge of the cliff the food needs to be placed so the log lands on the Road Runner. The rotating motion of the log in the air does not affect the motion of the log once it is in the air.…

The uniform solid block in the figure has mass 39.8 kg and edge lengths a = 0.902 m, b = 1.67 m, and c = 0.141 m. Calculate its rotational inertia about an axis through one corner and perpendicular to the large faces. Number:   Unit: