10) Find the center of mass and the moment of inertia about the y-axis of a thin plate bounded by the x-axis, the lines x = ±1, and the parabola y = x² if 8 (x, y) = 7y + 1. olution:)
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- 5) A disk of mass m = 75.0 g and radius r = 4.20 cm glides across an air table at a speed v = 1.5 m/s. It makes a glancing collision with a hoop of radius R = 5.80 cm and mass M = 130 g (initially at rest) such that their rims just touch. Because their rims are coated with instant-acting glue, the two objects stick together and rotate after the collision. a) What is the angular momentum of the system relative to the center of mass? b) What is the angular speed about the center of mass?two uniform solid spheres,A and B have the same mass.Each spbere,A and B has their own axis of rotation,the radius of sohere B is twice of sphere A.Which one of the following is true? (give I = 2/5mr^2) a)the moment of inertianof A IS 1/2 B b)the moment of inertianof A is 5/2 of B c) the moment of inertia of A is 1/4 B d)the two spheres have equal moments of inertia2) A uniform disk with mass 40.0 kg and radius 0.200 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 F = 30.0 N is applied tangent to the rim of the disk. (a) What is the magnitude of the tangential velocity of a point on the rim of the disk after the disk has turned through 0.200 revolution? (b) What is the magnitude of the resultant acceleration of a point on the rim of the disk after the disk has turned through 0.200 revolution?
- (5) For a body to be stationary in a frame of reference, what conditions must be met regarding forces and torques? Explain what not meeting each of the conditions will result in. (a) Show that the moment of inertia of a uniform thin rod (ruler, shaded grey below in figure) of length L and mass M rotating about its center is 1/12 ML² y (m)4 L/2 F -L/2 L/2 X (m) A constant tangential force of F-2 N (shown) is applied at the end to the initially stationary uniform thin rod of mass 2 kg and length L-6m pivoted about its center at the time t=0 s. This will rotate the rod. (b) Calculate the torque (Nm), and (c) the moment of inertia of the rod. (d) Calculate the angular acceleration of the rod (a rads/s²). (e) What is the angular displacement 0 at t = 1s (in radians and in degrees). (f) What is the angular velocity of the rod v at t = 1s. (g) What are the speeds of the tips of the rod at t = Is (they are the same). 0 -L/2 0 00The moment of inertia of the slab having mass m and length I about an axis passing through the center of mass (com) is Icom What is the moment of inertia about the axis of rotation shown in the fig? [4 minutes] 1/3 com 1/4 Axis of rotation Select one: mi O 1=com + com 16 com 3.9) A uniform cylinder of radius R, mass M, and length L rotates freely about a horizontal axis parallel to the cylinder and at the distance of 2R from is centert , as shown below. The moment of inertia of the cylinder about this axis is
- Number 12(a) Determine the centroidal polar moment of inertia of a circular area by direct integration. (b) Using the result of part (a), determine the moment of inertia of a circular area with respect to a diameter.10-105 Determine the moment of inertia of the compos- ite body shown in Fig. P10-105 with respect to the y-axis shown on the figure. The specific weiglıt of the material is 175 lb/ft. 3 in. 8 in. 6 in. 6 in. 6 in. . 6 in. 5 in. 8 in. 5 in. 12 in. 3 in. Fig. P10-105
- la) A “dumbbell" used in the energy conservation in rotational motion lab, consists of a cylindrical rigid rod with two 0.2 kg masses fixed at the ends. The mass of the rod is negligible when compared to the two masses. The diameter of the rod is 8 mm and its length is 20 cm. The rod is rotating about its center (with the axis of rotation perpendicular to the length of the rod as in today's experiment). What is the moment of inertia of this system?Find the moment of inertia about y-axis if each mass is equal to 1 kg (in kg×m2)