4. The wheel is composed of a 15kg hoop stiffened by four thin spokes, each with a mass of 2kg and radius r = 400mm. The wheel slips when a horizontal force P equal to or greater than 50N is applied to the wheel initially at rest. a) Calculate the static coefficient of friction. b) Calculate the linear velocity of the wheel's center after it has moved 2 meters with a constant force of P = 35N. P r 0
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- 11) A solid sphere, a uniform disk, and a hollow hoop all having identical masses and radii are started from rest at the top of an inclined plane simultaneously. The sphere reaches the bottom first. Using Newton's Laws and rotational dynamics show why this must be true. (Hint: Draw a FBD showing the forces present, and determine which are responsible for translation and which for rotation. I for the hoop MR', I for the disk is 1/2MR² and I for the solid sphere is 2/5MR?. Base you answer on the acceleration of the center of masses of each object.)a) Calculate the τx (torque) component in N m b) Calculate the τy component in N m c) Calculate the τz component in N m1. Which is larger for a hoop (ring) of mass M and radius R (I = MR²) that is rolling without slipping on a horizontal surface: its translational or its rotational kinetic energy? (a) Its translational kinetic energy. (b) Its rotational kinetic energy. (c) Both are the same. (d) The answer depends on the value of the radius. (e) The answer depends on the value of the mass.
- QUESTION 8 A horizontal, uniform, 8.00-kg, stationary, solid disk with a radius of 80.0 cm is pivoted at its center such that the plane of the disk is parallel to level ground. A boy applies a tangential force of 40.0 N on the disk by pulling on a rope that is inserted in a side groove of the disk. Through what total angle will the disk rotate 5.00 s? а. 156 rad b. 92.0 rad С. 108 rad d. 124 rad е. 140 radhaving negligible masses in the figure, and Solid rods running along the y-axis connect the three particles. If this system rotates around the x-axis with an angular velocity of 3.00 rad/s, what would be the total rotational kinetic energy? 4.00 kg y = 3.00 m 12 - 2.00 kg y - -2.00 m 3.00 kg y = -4.00 m A) 765 J B) 231 J C) 265 J D) 357 J E) 414 J2 Parts: a) Find the magnitude of torque needed to make such a change in RPM b) Find the tangential acceleration of a point P on the outer rim of disk
- 4. A uniform solid ball with mass m and radius R rolls smoothly along a floor, then up a ramp inclined at 37°. It momentarily stops when it has rolled 0.35 m along the ramp. What was its initial speed?Q2) A uniform disk with mass 38.2 kg and radius 0.240 m is pivoted at its center about a horizontal, frictionless axle that is stationary. The disk is initially at rest, and then a constant force 33.0 N is applied tangent to the rim of the disk. a) What is the magnitude v of the tangential velocity of a point on the rim of the disk after the disk has turned through 0.330 revolution? b) What is the magnitude a of the resultant acceleration of a point on the rim of the disk after the disk has turned through 0.330 revolution?Q. At t=3s, a point on the rim of a 0.200-m-radius Wheel has a tangential speed of 50m/s as the wheel slows down with a tangential acceleration of constant magnitude 10m/s2. Calculate the angular velocity at t=0 s? A) 250 rad/s B) 300 rad/s C) 350 rad/s D) 400 rad/s E) 450 rad/s
- Please helpA rectangular plate has width and breadth of 400 cm and 500 cm, respectively. An applied torque of 300 N.m gives the plate an angular acceleration of 15 rad/s² about a perpendicular axis through the centre of the plate. 1) Calculate the rotational inertia of the plate about that axis. [ 2) Determine the mass of the plate. 3) Suggest the radius of a solid sphere that has the same mass and rotational inertia as that of the plate. [1. For a long thin rod the linear density varies as λ ~ L^4 A. First calculate λ in terms of L and M (solve for the mass of the rod in terms of λ and L) B. Calculate the moment of inertia of a thin rod of mass M and length L around the left end which will be L= 0