Write down a typical moment of inertia term, and a typical product of inertia term, of the inertia tensor of a rigid body about its mass centre.
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- A massless cable is used to connect the center of mass of the cylinder A to the box B hanging over the pulley C. Take the coefficient of static friction as µs = 0.25 and that of kinetic friction as µk = 0.2. Assume that there is no slipping at the contact point D and solve the problem using Newton's second law to find: a) angular accelerations of the cylinder A and pulley C (aA and ac), b) tension forces in the cable on both sides of the pulley C (cylinder side is TA and box side is TB), and c) normal and rolling forces at D (Np and FD). d) Is the assumption of no slipping at the contact point D correct? Why or why not? Notes: 1) We are asuming that tension forces on two sides of the pulley C are not the same, but acceleration of the cable from A to B stays the same. 2) For a cylinder or disk of mass m and radius r, moment of inertia about its center is given as I = mr2/2. 3)Do not forget to sketch the FBD’s for the cylinder A, box B and pulley C. m, = 12 kg mc = 4 kg rc =0.2 m TA=0.5…A suspended homogeneous rod AB of length, 75 cm and mass of 5 kg is rotating about one of its ends (A) at an angular velocity of 10.24 rad s-1. 1). Calculate the moment of inertia I of this rod. 2) What is the corresponding linear velocity of the free end, B? 3) The end B hits and sticks to a ball of radius R=12.5 cm and mass 850 g moving in the opposite direction with a linear velocity of 5.48 m.s-1. Use the principle of conservation of momentum to find the linear velocity of the ball-rod system after the collisionA square trap door, of length and width 2m and mass 20kg, is heldopen at an angle of 65° with respect to the floor. A rope is attached to theraised edge of the door and fastened to the wall behind the door in such aposition that the rope pulls perpendicularly to the trap door. (a) What is thetorque exerted on the trap door by the rope? (b) What is the moment of inertiaof the door rotating on its hinge? (c) Suppose the rope is cut, causing the doorto slam shut, what angular acceleration would the door have right after therope was cut?
- Problem 5: Two blocks are connected with a rope as shown. The surfaces and the pulley are frictionless. The pulley is a disk with radius r and mass m,. A force F is applied to Mass 1 as F m1 shown so that Mass 1 accelerates to the left and Mass 2 accelerates upward. Take the positive direction to the be the direction of accelerations of the masses. (That is, the positive direction for Mass 1 is to the left, and the positive direction for Mass 2 is upward.) mp m2 In the space below, show how you would find the acceleration of the masses. Start with equations from the equation sheet and show your steps to the point where you would calculate the results. You do not need to calculate any numerical result. Just show how you would solve the problem. Be sure your equations reflect the positive direction as described above. Max characters allowed 3000. 0/3000A cord of negligible mass is wrapped around the outer surface of the 50-lb cylinder and its end is subjected to a constant horizontal force of P = 2 lb as shown in (Figure 1). Take r = 0.9 ft. Figure 1 of 1 P = 2 lb Part A If the cylinder rolls without slipping at A, determine its angular velocity in 5 s starting from rest. Neglect the thickness of the cord. Express your answer in radians per second to three significant figures. IVE ΑΣΦ | 11 Submit Request Answer < Return to Assignment vec Provide Feedback p ? rad/sA 7.5-kg uniform cylindrical roller (radius 0.50 m), initially at rest, is acted upon by a 25N rightward force, applied on its center of gravity. The body rolls without slipping over a distance of 8 m. The mass moment of inertia of a cylinder about its centroidal longitudinal axis is 1/2 mr2 a) determine the magnitude and direction of the constant angular acceleration of the cylinder as it rolls over the horizontal platform.
- In order for an object to roll smoothly (with constant angular acceleration) down a ramp, it must have either spherical or cylindrical symmetry. Consider spherically and cylindrically symmetric objects with mass M and outer radius R rollingwithout slipping down an incline of height h and angle θ from the horizontal. The rotational inertias of such objects can be written in the generalized form: ? = ???2, where c is a shape factor whose value depends on the geometry of the object. (If you look at the table of rotational inertias in the textbook you’ll be able to see that this is true.)(For this question, consider M, R, c, h, θ, and g as the given quantities—express your answers in terms of some or all of these quantities. Simplify your answers as much as you can.)a. If the object starts from rest at the very top of the ramp before rolling freely down the ramp without slipping, find the object’s (linear) speed at the bottom of the ramp.(Hint: use conservation of energy.)??????? =…PLEASE HELP(a) Explain what a principal axis system for a rigid body is. (b) Write down the definition of the moment of inertia of a rigid body with respect to a fixed axis ñ. (c) If the principal moments of inertia of a rigid body are all equal, I₁ = I₂ = I3, does that imply that the mass-distribution p(x) in the rigid body is spherically symmetric? Give a short explanation. (d) State what a normal mode is.