![]() ![]() Three forces are exerted on the rod with the magnitudes and directions shown in the figure. A rod is initially at rest on a rough horizontal surface. Determine the area bound by the curve and the horizontal axis from 0s to 6s, because the shape of the curve on the graph will be a right triangle and the area can be directly determined. Create a graph of net torque as a function of time and graph four points of data by using the table. How can a student use the data table to determine the change in angular momentum of the object from 0s to 6s? Justify your selection. The table shows the net torque exerted on the object at different instants in time. A net torque is applied to the edge of a spinning object as it rotates about its internal axis. This procedure can be used because ΔL=τΔt with τ=rF. Determine the vertical intercept, multiply the result by 0.25m, and then multiply that result by 8s. How can a student use the graph to determine the change in angular momentum of the disk after 8s? Justify your selection. The net force is applied tangent to the edge of the disk. A graph of the net force as a function of time for the edge of the disk is shown. Vertical Speed - Makes a triangle A net force is applied to the edge of a disk that has a diameter of 0.5m. Which of the following pairs of graphs best represents the angular speed as a function of time for the pulley and the vertical speed as a function of time for the falling object for a short time after it is released from rest? Angular Speed - Makes a half trapezoid The object is released from rest and it falls to the floor at time t1. D) ω0t0+12α0t20+(ω0+α0t0)t1 An object of mass M hangs from a string that is looped around a pulley of negligible friction, as shown. What is the angular displacement of the point from t=0 to t=t1? Express your answer in terms of ω0, α0, t0, t1, and/or any fundamental constants as appropriate. The point then rotates at a constant angular speed until time t=t1. A point on a rotating object has an initial angular velocity ω0 and rotates with an angular acceleration α0 for a time interval from t=0 to time t=t0. Based on the data, if possible, how could the student predict the angular displacement of a point on the edge of the disk from time ts until the disk no longer rotates if the initial angular speed is increased to 2ωd ? Justify your selection. The angular acceleration of the disk is determined to be αd, and this value remains constant. ![]() A student measures the angular displacement Δθ0 of a point on the edge of the disk from time ts until the disk no longer rotates. At time ts, the disk rotates about the center axle with an initial angular speed wd. Frictional forces between the axle and the supports is not negligible. Which of the following predictions is correct about the motion of the system containing the rod and all three spheres of clay immediately after the collision?Ī disk is fixed to a horizontal axle that extends between two supports, as shown in the figure. ![]() The time of collision with the rod for each sphere is time t0. All three spheres of clay are launched with the same initial linear speed and collide with the rod at the same time. Consider the situation in which three identical spheres of clay are launched simultaneously, one along each possible path. Frictional forces are considered to be negligible. A pivot is fixed to the end of the rod, representing the point at which the rod or clay-rod system may rotate. In each case, the time of collision between the sphere of clay and the rod is time t0. In each case, the sphere of clay is launched with the same linear speed and sticks to the rod. ![]() Path X and path Z are directed toward the center of mass of the rod. A student may launch a sphere of clay toward the rod along one of the three paths shown in the figure. What is the angular speed ωf of the clay-rod system immediately after the collision?Ī uniform rod is at rest on a horizontal surface. The sphere of clay is considered to be a point mass. The rotational inertia of the rod about the joint is IR, and the mass of the sphere of clay is mc. The sphere of clay is launched with a speed v0 and collides with the rod a distance l away from the pivot. Consider the case in which the sphere of clay is launched along path Y. A uniform rod is at rest on a horizontal surface. ![]()
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