4) Figures 4A (side view) and 4B (overhead view) illustrates a uniform solid cylinder having mass...
4) Figures 4A (side view) and 4B (overhead view) illustrates a uniform solid cylinder having mass M and radius R. The cylinder is positioned on a horizontal floor having sufficient friction to ensure that the cylinder can roll without slipping. The cylinder includes a mass-less yoke that is fixed to the symmetric axis of the cylinder and acts as a rolling friction-less pivot for the cylinder. An ideal spring having spring constant K is attached to the yoke at one...
The figure on the right illustrates a ball which is a uniform solid sphere having mass M and radius R. The ball is initially traveling in the positive direction with pure translational motion along a friction-less region of a horizontal surface (i.e. it slips with angular speed ω0-0). The initial translational speed of the ball is Vo. The friction-less region extends to a region having coefficient of kinetic friction Figure for WAH #10 V. Friction Friction-less No longer slipping '...
A uniform, solid cylinder with mass 3M and radius 2R rests on a
horizontal tabletop. A string is attached by a yoke to a
frictionless axle through the center of the cylinder so that the
cylinder can rotate about the axle. The string runs over a
disk-shaped pulley with mass M and radius R that is mounted on a
frictionless axle through its center. A block of mass M is
suspended from the free end of the string (the figure...
We wrap a light, flexible cable around a solid cylinder with mass 0.68 kg and radius 0.17 m . The cylinder rotates with negligible friction about a stationary horizontal axis. We tie the free end of the cable to a block of mass 1.42 kg and release the object with no initial velocity at a distance 1.63 m above the floor. As the block falls, the cable unwinds without stretching or slipping, turning the cylinder. Suppose the falling mass is made of ideal rubber,...
A solid sphere and a hollow cylinder of the same mass and radius have a rolling race down an incline as in Example 13.9. They start at rest on an incline at a height habove a horizontal plane. The race then continues along the horizontal plane. The coefficient of rolling friction between each rolling object and the surface is the same. Both have mass M Both have radius R. Write an expression for the distances that each object will roll...
2. A uniform, solid cylinder with mass M and radius 2R is on an incline plane with angle of inclination of 6. A string is attached by a yoke to a frictionless axle through the center of the cylinder so that the cylinder can rotate about the axle. The string runs over a disk-shaped pulley with mass M and radius R that is mounted on a frictionless axle through its center. A block of mass M is suspended from the...
A light cable is wrapped around a solid cylinder with mass M = 1.50 kg and radius R = 0.20 m as shown in the figure below. The cylinder rotates with negligible friction about a stationary horizontal axis. The free end of the cable is tied to a block of mass m = 0.50 kg. The block, initially at rest, is released at a height h = 1.00 m above the floor. As the block falls, the cable unwinds without...
A uniform cylinder of radius r15.0 cm and mass m 1.70 kg is rolling without slipping on a horizontal tabletop. The cylinder's center of mass is observed to have a speed of 4.60 m/s at a given instant. (a) What is the translational kinetic energy of the cylinder at that instant? J (b) What is the rotational kinetic energy of the cylinder around its center of mass at that instant? J (c) What is the total kinetic energy of the...
Bridging Problem: Oscillating and Rolling Two uniform, solid cylinders of radius R and total mass M are connected along their common axis by a short, light rod and rest on a horizontal tabletop (Figure 1). A frictionless ring at the rod's center is attached to a spring of force constant k, the spring's other end is fixed. The cylinders are pulled to the left a distance I, stretching the spring, then released from rest. Due to friction between the tabletop...
1) A rope of negligible mass passes over a uniform cylindrical pulley of 1.50 kg mass and 0.090 m radius. The bearings of the pulley have negligible friction, and the rope does not slip on the pulley. On one end of the rope hangs a 3.00 kg bunch of bananas, and on the other end hangs a 4.50 kg monkey. Calculate the downward acceleration of the monkey and the tension in both ends of the rope. 2) A 200 g...