Find the moment of inertia of a thin uniform rod of mass Mand length L about an axis passing through its centre and making an angle 0 with the rod.
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- A solid, uniform disk of radius 0.250 m and mass 55.0 kg rollsdown a ramp of length 4.50 m that makes an angle of 15.0°with the horizontal. The disk starts from rest from the top ofthe ramp. Find (a) the speed of the disk’s center of mass whenit reaches the bottom of the ramp and (b) the angular speedof the disk at the bottom of the ramp.The uniform thin rod in the figure below has mass M = 2.00 kg and length L = 3.25 m and is free to rotate on a frictionless pin. At the instant the rod is released from rest in the horizontal position, find the magnitude of the rod's angular acceleration, the tangential acceleration of the rod's center of mass, and the tangential acceleration of the rod's free end.A solid cylinder of uniform density of radius 2 cm has mass of 50 g. If its length is 10 cm, Calculate its moment of inertia about (i) its own axis of rotation passing through the centre. (ii) an axis passing through its centre and perpendicular to its length.
- A solid, horizontal cylinder of mass 10.0 kg and radius 1.00 mrotates with an angular speed of 7.00 rad/s about a fixedvertical axis through its center. A 0.250-kg piece of putty isdropped vertically onto the cylinder at a point 0.900 m fromthe center of rotation and sticks to the cylinder. Determinethe final angular speed of the system.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 uniform, thin, solid door has height 2.35 m, width 0.855 m, and mass 25.0 kg. (a) Find its moment of inertia for rotation on its hinges. kg · m2 (b) Is any piece of data unnecessary? (Select all that apply.) The height of the door is unnecessary. O The width of the door is unnecessary. O The mass of the door is unnecessary. O No; all of the data is necessary.
- A uniform beam of length, L, and mass, M, is freely pivoted at one end about an attachment point in a wall. The other end is supported by a horizontal cable also attached to the wall, so that the beam makes an angle phi with the horizontal as shown below. To answer the questions below, find algebraic expressions for the tension in the cable, the angular acceleration of the beam, should the cable break, and the resulting angular velocity as the beam falls through the vertical position. If L = 1.8 m, M = 15 kg, and phi = 30o, then what is the tension in the cable? If the cable snaps, what is the angular acceleration about the pivot point? What is the angular velocity of the falling beam, just as it hits the wall?A torque of 0.97 N*m is applied to a bicycle wheel of radius 35 cm and mass 0.75 kg. Treating the wheel as a hoop, find its angular acceleration.A uniform beam of length, L, and mass, M, is freely pivoted at one end about an attachment point in a wall. The other end is supported by a horizontal cable also attached to the wall, so that the beam makes an angle phi with the horizontal as shown below. To answer the questions below, find algebraic expressions for the tension in the cable, the angular acceleration of the beam, should the cable break, and the resulting angular velocity as the beam falls through the vertical position. If L = 0.7 m, M = 10 kg, and phi = 35º, then what is the tension in the cable? If the cable snaps, what is the angular acceleration about the pivot point? 17.20219293 rad/s^2 What is the angular velocity of the falling beam, just as it hits the wall?