A uniform thread of linear mass density 1 = 2.0 g/m passes through a fixed ideal pulley. At its ends, the thread is stacked into two heaps that do not interfere motion of the thread. A beetle of mass m = 80 g tries to manage itself at a constant height on the thread by adjusting its speed relative to the thread. At some steady speed of the thread, the beetle succeeds in doing so. Find this steady speed of the thread. Acceleration due to gravity is g = 10 m/s².

Calculate the magnitude of the cross product of the following two vectors: b = 2j + 5k = (0 ,2,5) å = 1î + 3ĵ = (1,3,0) , b= 2ĵ + 5k = (0 ,2 , 5)

Joe's shoulder is labeled S and two points on the cable are labeled P and B. The coordinates of the three points are given below and the tension in the cable is 200 N. Find the moment about Joe's shoulder. Point S P B X (m) 0.68 0 1.9 Y (m) 0.9 3.2 1.1 z (m) 1.4 0 1.4

A thin rod of length 0.632 m and mass 66.5 g is suspended freely from one end. It is pulled to one side and then allowed to swing like a pendulum, passing through its lowest position with angular speed 1.35 rad/s. Neglecting friction and air resistance, find (a) the rod's kinetic energy at its lowest position and (b) how far above that position the center of mass rises.

A block of wood is attached to a very lightweight metal rod, which is attached to a fixed pivot point on a table. The block is able to slide on the table with negligible friction, and the pivot is also free to rotate with negligible friction. The block's mass is M and the rod's length is ℓ. A bullet is moving parallel to the table and perpendicular to the rod when it collides and embeds within the block. The bullet's speed just before entering the block is v and its mass is m. (a) Find the angular momentum of the combined bullet–block system about the vertical pivot axis. (Use any variable or symbol stated above as necessary. Enter the magnitude.) L=----   (b) Find the fraction of the original kinetic energy of the bullet that is converted into internal energy within the bullet-block system during the collision. (Use any variable or symbol stated above as necessary.)

A circular disc of mass M and radius R is rotating about its axis with angular speed ω1 . If another stationary disc having radius R/2 and same mass M is droped co-axially on to the rotating disc. Gradually both discs attain constant angular speed ω2. The energy lost in the process is p% of the initial energy. Value of p is

A uniform rod with a mass of 100 g and a length of 50.0 cm rotates in a horizontal plane about a fixed vertical, frictionless pin passing through the center of the rod. Two small beads, each having a mass of 30.0 g, are mounted on the rod so that they are able to slide without friction along its length. Initially, the beads are held by catches at positions 10.0 cm on each side of the rod’s center; at this time, the system rotates at an angular speed of 20.0 rad/s. Suddenly, the catches are released, and the small beads slide outward along the rod. Find (a) the angular speed of the system at the instant the beads reach the end of the rod and (b) the angular speed of the rod after the beads fly off the rod’s ends.

Kathrine lets go of a cube of mass of m = 5 kilograms on her physics demo device she created. Her cube goes down a super smooth slide surface that has a height vertical distance of h=85 cm. At the end of the slide, her cube crashes into and sticks to the lower end of a vertical pole that has a mass M=10.5 kg and length 1-2.00m. Right after the crash, the pole pivots about a hinge point near its upper end through an angle (theta) before it stops for a moment. See the image given below to visualize Katherines system. You are tasked with Figuring out the following three things The speed of her cube just before it hits the pole The angular speed of the pole just after the crash The angle (theta) through which the pole pivots a. b. C. 0 Kathrine and her device

In the figure, a small 0.131 kg block slides down a frictionless surface through height h = 0.815 m and then sticks to a uniform vertical rod of mass M = 0.262 kg and length d = 2.20 m. The rod pivots about point o through angle before momentarily stopping. Find 0. A ₂ 0

At the instant of the figure, a 7.70 kg particle P has a position vector of magnitude 6.70 m and angle 0₁ = 49.0° and a velocity vector of magnitude 8.90 m/s and angle 0₂ = 29.0°. Force F, of magnitude 9.80 N and angle 03 = 29.0° acts on P. All three vectors lie in the xy plane. About the origin, what are the magnitude of (a) the angular momentum of the particle and (b) the torque acting on the particle? (a) Number i (b) Number Units Units V. 0 0₂