Four particles, each of mass 0.39 kg, are placed at the vertices of a square with sides of length 0.57 m. The particles are connected by rods of negligible mass. This rigid body can rotate in a vertical plane about a horizontal axis A that passes through one of the particles. The body is released from rest with rod AB horizontal, as shown in the figure. (a) What is the rotational inertia of the body about axis A? (b) What is the angular speed of the body about axis A at the instant rod AB swings through the vertical position? Rotation axis B (a) Number Units (b) Number i Units

A wheel of radius 0.35 m rotates in a clockwise sense about a fixed axle with negligible friction at an initial angular speed of 2.6 rad/s. The wheel's mass of 17 kg is concentrated in its rim. You apply a clockwise torque to the rotating wheel by pushing on the rim tangentially with a constant force of 22 N. Find the wheels angular speed, in radians per second, 0.085 seconds after you start pushing on the rim.

A uniform disk of mass m = 1.4 kg and radius R = 25 cm can rotate about an axle through its center. Four forces are acting on it as shown in the figure. Their magnitudes are F1 = 3.5 N, F2 = 3.5 N, F3 = 7.5 N and F4 = 3.5 N. F2 and F4 act a distance d = 2.5 cm from the center of mass. These forces are all in the plane of the disk. m = 1.4 kgR = 25 cmF1 = 3.5 NF2 = 3.5 NF3 = 7.5 NF4 = 3.5 Nd = 2.5 cm Write an expression for the magnitude τ1 of the torque due to force F1.  Calculate the magnitude τ1 of the torque due to force F1, in N⋅m.     Write an expression for the magnitude τ2 of the torque due to force F2.    Calculate the magnitude τ2 of the torque due to force F2, in N⋅m.   Write an expression for the magnitude τ3 of the torque due to force F3.     Write an expression for the magnitude τ4 of the torque due to force F4.     Calculate the magnitude τ4 of the torque due to force F4, in N⋅m.     Calculate the angular acceleration α of the disk about its center of mass in rad/s2. Let…

A uniform rod of mass 2.20 kg and length 2.00 m is capable of rotating about an axis passing through its center and perpendicular to its length. A mass m1 = 4.50 kg is attached to one end and a second mass m2 = 2.60 kg is attached to the other end of the rod. Treat the two masses as point particles.(a)What is the moment of inertia of the system in kg · m2?   (b)If the rod rotates with an angular speed of 2.70 rad/s, how much kinetic energy, in joules, does the system have?   (c)Now consider the rod to be of negligible mass. What is the moment of inertia of the rod and masses combined, in kg · m2?   (d)If the rod is of negligible mass, what is the kinetic energy, in joules, when the angular speed is 2.70 rad/s?

A 20-kg piece of steel pipe that is 20 cm in diameter, 80 cm long, and 1 cm thick is rolling toward you at a speed of 3.0 m/s.   (a)What is the magnitude and direction of the pipe’s angular velocity vector w?   (b)What is the pipe’s rotational energy?  (c) What is its total energy K + Urot?

A solid cylinder with mass m, radius R, and rotational inertia I (about its center) is released from rest and rolls down a ramp.  Friction between the bottom of the cylinder and the ramp causes the cylinder to roll without slipping.  The linear acceleration of the cylinder is a.  Which TWO of the equations below are correct for this scenario? The equations are in terms of m, I, R, and a, as well as f (the force of static friction between the cylinder and the ramp) and g.  (You must pick BOTH of them to get this question correct!) f = ma mg sin θ = ma mg sin θ - f = ma f R = I (a/R) mg sin θ - f = I (a/R) R mg sin θ = IaR

A uniform disc of mass 3.0 kg and radius 25 cm is mounted on a fixed horizontal axle. A block with mass 1.8 kg hangs from a light cord that is wrapped around the rim of the disc. What is the angular acceleration of the disc?

The figure shows an arrangement of 15 identical disks that have been glued together in a rod-like shape of length L = 1.4600 m and (total) mass M = 160.0 mg. The arrangement can rotate about a perpendicular axis through its central disk at point O. (a) What is the rotational inertia of the arrangement about that axis? Give your answer to four significant figures. (b) If we approximated the arrangement as being a uniform rod of mass M and length L, what percentage error would we make in using the formula in Table 10-2e to calculate the rotational inertia? ooooooooooo (a) Number i (b) Number i Units Units

Two wheels A and B in the figure are connected by a belt that does not slip. The radius of B is 4.30 times the radius of A. What would be the ratio of the rotational inertias IA/IB if the two wheels had (a) the same angular momentum and (b) the same rotational kinetic energy? (the absolute tolerance for the answer of a is ± 0.001)(the absolute tolerance for the answer of b is ± 0.0001)

In the figure, two particles, each with mass m = 0.88 kg, are fastened to each other, and to a rotation axis at 0, by two thin rods, each with length d = 5.6 cm and mass M = 1.3 kg. The combination rotates around the rotation axis with angular speed w = 0.28 rad/s. Measured about O, what is the combination's (a) rotational inertia and (b) kinetic energy? M. M. Rotation axis (a) Number i Units (b) Number i Units