I+mR, R2 f = I+mR,2 (b) Determine the direction of the force of friction. Figure P10.45 Ri

A spool of thread consists of a cylinder of radius R₁ = 4.5 cm with end caps of radius R₂ = 9.0 cm as depicted in the end view shown in the figure below. The mass of the spool, including the thread, is m = 280 g. The spool is placed on a rough, horizontal surface so that it rolls without slipping when a force T= 0.620 N acting to the right is applied to the free end of the thread. For the moment of inertia treat the spool as being a solid cylinder of radius R₁, as the extended edges are thin and therefore light. (a) What is the acceleration of the spool? Take positive to be to the right. .739 m/s² (b) Determine the direction of the force of friction. to the left to the right straight up straight down

A window cleaner is pulling himself up to a pulley that consists of two disks welded together as shown. The person is currently pulling straight down on the rope in his hands with a force of magnitude 482.9 N. The other rope is also vertical and is attached to the person's center of mass. The person's mass is 72.2 kg, the pulley's total moment of inertia is 2.88 kg⋅m2, the radius of the small disk is 0.32 m, and the radius of the big disk is 0.60 m.What is the magnitude of the acceleration of the person's center of mass?

The outstretched hands and arms of a figure skater preparing for a spin can be considered a slender rod pivoting about an axis through its center ( Ibar=ml² where l is the length of the bar). When the skater's hands and arms are brought in and wrapped around their body to execute the spin, the hands and arms can be considered a thin-walled hollow cylinder. The hands and arms have a combined mass 10 kg. When outstretched, they span 2.1 m. When wrapped, they form a cylinder of radius 21 cm. The moment of inertia about the rotation axis of the remainder of the body is constant and equal to 0.6 kg-m2. If the original angular speed is 0.5 rev/s, what is the final angular speed? 00f= rev/s Determine how much the figure skater's rotational KE increased. [NOTE: We express energy in J. To get J, you must convert your angular velocities to the appropriate mks. units which are rad/s.] ΔΚΕ- =

Two Thin rectangular sheets (0.28m x 0.47 m) are identical. In the first sheet the axis of rotation lies along the 0.28 inside, and in the second it lies along 0.47m side. The same torque is applied to each sheet. The first sheet starting from rest reaches its final angular velocity in 5.2 s. How long does it take for the second seat starting from rest to reach the same Angularer velocity?

A top is a toy that is made to spin on its pointed end by pulling on a string wrapped around the body of the top. The string has a length of 63 cm and is wrapped around the top at a place where its radius is 2.0 cm. The thickness of the string is negligible. The top is initially at rest. Someone pulls the free end of the string, thereby unwinding it and giving the top an angular acceleration of +14 rad/s2. What is the final angular velocity of the top when the string is completely unwound?

A top is a toy that is made to spin on its pointed end by pulling on a string wrapped around the body of the top. The string has a length of 52 cm and is wrapped around the top at a place where its radius is 2.2 cm. The thickness of the string is negligible. The top is initially at rest. Someone pulls the free end of the string, thereby unwinding it and giving the top an angular acceleration of +11 rad/s². What is the final angular velocity of the top when the string is completely unwound? Number Before string is pulled After string is pulled Units

A solid cylinder with mass m, radius R, and rotational inertia I (about its center) is released from rest and rolls down a ramp.  Friction between the bottom of the cylinder and the ramp causes the cylinder to roll without slipping.  The linear acceleration of the cylinder is a.  Which TWO of the equations below are correct for this scenario? The equations are in terms of m, I, R, and a, as well as f (the force of static friction between the cylinder and the ramp) and g.  (You must pick BOTH of them to get this question correct!) f = ma mg sin θ = ma mg sin θ - f = ma f R = I (a/R) mg sin θ - f = I (a/R) R mg sin θ = IaR

Please answer E16,E17

Two disks are initially spinning, one above the other on a small axle that provides a small, but non-negligible torque from friction, as shown in the figure below. Both disks have the same radius, R = 2.58 m. Disk 1 has a moment of inertia I1 = 9.8 kg⋅m2. Disk 2 has a moment of inertia I2 = 5 kg⋅ m2. Let vertically up be the z direction, such that counterclockwise rotation as viewed from above corresponds to positive values of the z-component. Disk 1 is initially spinning with a z-component of angular velocity ω1,z = 21 rad/s, and disk 2 is initially spinning with a z-component of angular velocity ω2,z = -15 rad/s. The z component of their common angular velcoity is 8.837 rad/s How much thermal energy is created in the process of disk 1 falling on disk 2 such that they reach a common final angular velocity? You do not need to worry about the gravitational potential energy because the initial separation of the disks is small. I get I need to use kinetic energy equations of 1/2*I*w2 but…