The uniform square steel plate has a mass of 7 kg and is resting on a smooth horizontal surface in the x-y plane. If a horizontal force P = 101 N is applied to one corner in the direction shown, determine the magnitude of the initial acceleration of corner A. The distance b = 235 mm.

Shown below is a small particle of mass 20 g that is moving at a speed of 10.0 m/s when it collides and sticks to the edge of a uniform solid cylinder. The cylinder is free to rotate about its axis through its center and is perpendicular to the page. The cylinder has a mass of 0.5 kg and a radius of 10 cm, and is initially at rest. (a) What is the angular velocity of the system after the collision? (b) How much kinetic energy is lost in the collision?

A long, uniform rod of length L and mass M is pivoted about a frictionless, horizontal pin through one end. The rod is released from rest in a vertical position as shown in Figure P10.65. At the instant the rod is horizontal, find (a) its angular speed, (b) the magnitude of its angular acceleration, (c) the x and y components of the acceleration of its center of mass, and (d) the components of the reaction force at the pivot. Figure P10.65

Find the net torque on the wheel in Figure P10.23 about the axle through O, taking a = 10.0 cm and b = 25.0 cm. Figure P10.23

Pls answer all three questions. One is the file attached. The second question is 2. Calculate the moment of inertia of the array of point objects shown in the figure about the horizontal axis. Assume m = 2.1 kg , M = 3.3 kg , and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.Express the answer in 2 sig figs. 3. About which axis would it be harder to accelerate this array? x or y?

A sitting person is pulling a rope with a force F. The working line of the pulling force runs through the point S. On the torso, a gravitational force G is also working, which can be assumed to act on point M. The following points are given, with respect to the basis {ex, ēy, ēz}. 3.9 Xo = 30ex + 30ey [cm] IM = 20ex + 50ey [cm] Is = 10ex + 70ey [cm] point O: point M: point S:

Lily is a 50 kg diver. At the instant of takeoff, her angular momentum about her longitudinal axis is 20 kgm2/s. Her radius of gyration about the longitudinal axis is 0.4 m at this instant. During the dive, Lily tucks and reduces her radius of gyration about the longitudinal axis to 0.2 m.a. At takeoff, what is Lily’s moment of inertia about her longitudinal axis?b. At takeoff, what is Lily’s angular velocity about her longitudinal axis?c. After Lily tucks, what is her moment of inertia about her longitudinal axis?d. After Lily tucks, what is her angular velocity about her longitudinal axis?

A uniform door weighs 46.00 N and is 0.9000 m wide and 2.800 m high. What is the magnitude of the torque due to the door's own weight about a horizontal axis perpendicular to the door and passing through a corner? N m

An steel plate of mass 0.882 kg has the shape of the isosceles triangle shown. The moment of inertia of the plate about its center of mass is 0.0055 kg.m2. The dimensions of the triangle are a = 0.435 m and b = 0.286 m. a. What are the coordinates of the center of mass? xcm =  ycm =   b. Calculate the moment of inertia of the steel plate for rotation about a perpendicular axis passing through the origin. I0 =

In this system, the rope and pulley have negligible mass and the pulley is frictionless. m1 a. F R m₂ The blocks have masses m₁ = 4.44 kg and m₂ = 10.8 kg and the coefficient of kinetic friction between m₁ and the surface is μ = 0.235. In addition, the pulley has a mass M = 3.71 kg and a moment of inertia about its center described as I = 0.537 MR². We will apply a constant leftward force of F = 42 N to m₁. Initially, the system is essentially at rest. What is the magnitude of acceleration for the blocks?