A solid sphere, shown in Figure 3, has radius R = 0.25 m and mass M = 20 kg. The line AB passes through the center of the sphere. The sphere is initially at rest. A constant torque is applied to the sphere, causing it to rotate as shown. The magnitude of torque, about axis AB, is t = 10 N · m. No other torques act on the sphere. Suppose this constant torque is applied until the sphere has rotated through an angle of 5 radians. Calculate the sphere's angular velocity. In other words, what is the final angular velocity of the sphere after it has rotated through an angle of 5 radians under a constant torque of 10 N · m? %3D A M R B

Two spheres are each rotating at an angular speed of 21.9 rad/s about axes that pass through their centers. Each has a radius of 0.190 m and a mass of 1.34 kg. However, as the figure shows, one is solid and the other is a thin-walled spherical shell. Suddenly, a net external torque due to friction (magnitude = 0.380 N · m) begins to act on each sphere and slows the motion down. How long does it take (a) the solid sphere and (b) the thin-walled sphere to come to a halt?  Can someone please help?

A force of 35 N is applied tangentially to the rim of a solid disk of radius 0.18 m. The disk rotates about an axis through its center and perpendicular to its face with a constant angular acceleration of 120 rad/s2. Determine the mass of the disk.

A uniform thin rod of mass m = 3.2 kg and length L = 1.7 m 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 = 4.5 N, F3 = 15 N and F4 = 17 N. F2 acts a distance d = 0.21 m from the center of mass.Calculate the magnitude τ1 of the torque due to force F1, in newton meters. τ1 = Calculate the magnitude τ2 of the torque due to force F2 in newton meters. τ2 = Calculate the magnitude τ3 of the torque due to force F3 in newton meters. τ3 = Calculate the magnitude τ4 of the torque due to force F4 in newton meters. τ4 =Calculate the angular acceleration α of the thin rod about its center of mass in radians per square second. Let the counter-clockwise direction be positive. α =

A small object with mass 3.95 kg moves counterclockwise with constant angular speed 1.65 rad/s in a circle of radius 3.45 m centered at the origin. It starts at the point with position vector 3.45î m. Then it undergoes an angular displacement of 8.55 rad. (a) What is its new position vector? m (b) In what quadrant is the object located and what angle does its position vector make with the positive x-axis? ---Select-- Vat o (c) What is its velocity? m/s (d) In what direction is it moving? (Give a negative angle.) ° from the +x direction. (e) What is its acceleration? m/s² (f) What total force is exerted on the object? N

What force does the water exert (in addition to that due to atmospheric pressure) on a submarine window of radius 26 cm at a depth of 7100 m in sea water (density 1025 kg/m3)? 4.82 x 105 N O 1.51 x 1011 N O 7.57 x 10 N O 7.57 x 10 N O 1.51 x 107 N

To study torque experimentally, you apply a force to a beam. One end of the beam is attached to a pivot that allows the beam to rotate freely. The pivot is taken as the origin or your coordinate system. You apply a force of F = Fx i + Fy j + Fz k at a point r = rx i + ry j + rz k on the beam. Part (a)  Enter a vector expression for the resulting torque, in terms of the unit vectors i, j, k and the components of F and r.  Part (b)  Calculate the magnitude of the torque, in newton meters, when the components of the position and force vectors have the values rx = 4.42 m, ry = 0.015 m, rz = 0.035 m, Fx = -4.2 N, Fy = 6.6 N, Fz = 2.8 N.   Part (c)  If the moment of inertia of the beam with respect to the pivot is I = 368 kg˙m2, calculate the magnitude of the angular acceleration of the beam about the pivot, in radians per second squared.

A uniform rod of mass M=6 kg and length L=3 m with a particle of mass m=2 kg attached to its one end rotates in the xy plane about a fixed axis oriented parallel to the z-axis through the other end. At an instant when the rod makes an angle θ=20o with the x-axis, the magnitude of the angular acceleration of the particle- rod system is: A). 0.80 rad/s2 B). 0.62 rad/s2 C). 0.31 rad/s2 D). 0.4 rad/s2

One end of a meter stick is pinned to a table, so the stick can rotate freely in a plane parallel to the tabletop. Two forces, both parallel to the tabletop, are applied to the stick in such a way that the net torque is zero. The first force has a magnitude of 2.00 N and is applied perpendicular to the length of the stick at the free end. The second force has a magnitude of 6.00 N and acts at a 38.9° angle with respect to the length of the stick. Where along the stick is the 6.00-N force applied? Express this distance with respect to the end of the stick that is pinned. d= i >

An object has a moment of inertia of 10.82 k g ⋅ m 2, and a torque of 19.1 N ⋅ m is applied on it. What is the angular acceleration of the object in unit of rad/s?