t B In the figure, wheel A of radius rA is coupled by belt B to wheel C of radius rc. The angular speed of wheel A is increased from rest at a constant rate a. Find the time needed for wheel C to reach angular speed wassuming the belt does not slip. (Hint: If the belt does not slip, the linear speeds at the two rims must be equal.) NOTE: Express your answer in terms of the given variables. w rc ΤΑ a TC X
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- A linkage undergoing motion as shown. The velocity of the block, vp, is 4 m/s. The length of the rods is l=0.5m. l 45° -90° 45° l 121 No What are the angular velocities of links AB and BD in rad/s. Note: They both have the same angular velocity due to the symmetric geometry. Give your answer with 2 decimals.Now let's use conservation of energy to calculate the kinetic energy of a rotating cylinder. Specifically, we will employ the work-energy theorem to relate the work done on the cylinder to the change in its rotational kinetic energy. A light, flexible, nonstretching cable is wrapped several times around a winch drum-a solid cylinder with mass 50 kg and diameter 0.14 m that rotates about a stationary horizontal axis turning on frictionless bearings (Figure 1). The free end of the cable is pulled with a constant force of magnitude 9.7 N for a distance of 2.0 m. It unwinds without slipping, turning the cylinder as it does so. If the cylinder is initially at rest, find its final angular velocity w and the final speed v of the cable. Figure F 2.0 m 50 kg 1 of 2 SET UP (Figure 2) shows our sketch for this problem. SOLVE No energy is lost due to friction, so the final kinetic energy K = Iw² of the cylinder is equal to the work W = F's done by the force (of magnitude F, pulling through a…Question in pic.
- Start with a freely rotating hoop-like wheel of mass m = 30kg and radius 25cm, rotating at 125 rpm.1. Sketch this wheel, write out equations for and calculate it’s L and rotational KE.The wheel hits the ground, bounces and skids while negative accelerating, eventually locking to the ground so that its linear velocity equals its rotational velocity times its radius.2. Write this (roll no slip) equation. Sketch this final rolling wheel on the ground, include a vector for the linear velocity.3. Write an equation conserving angular momentum before and after the drop. Solve your equation for final angular velocity (both algebra and a number). Briefly explain.4. Solve for final rotational and linear kinetic energy and compare to initial rotational energy. How much energy was lost during the skidding process? (Formula and number).consider the figure above. consider the small block (M). let say that this inverted cone is rotating vertically or a vertical axis. lets say that the angular speed of this is Vtangential = = r*@ coefficient static friction (block and xone) = Hs. LETS SAY we need to remain this block at its height while spinning (radius of revolution = h*tan theta), FIND: a. Max value of b. min value ofAsmall cube (M = 0.45 kg) is at a height of 315 cm up a frictionless track which has a loop of radius, R= 47.25 cm at the bottom. The %3D cube slides freely down the ramp and around the loop. Find the velocity of the block when it is at the top of the loop. V H R
- In a specific ballet move called pirouette, the ballerina spins on her toes. She can control the speed of the spin by adjusting the position of her arms and legs. [ Note: you can consider model the ballerina with her arms and legs tucked in a uniform cylinder of mass 55 kg and radius 13 cm.] You can understand the axis of rotation of her spin, right? Let's consider for the last t= 15 sec, she is spinning with a constant angular speed o = 7/3 rad/s. Which of the following is true regarding the tangential acceleration of her spin? (a) Tangential acceleration is zero for the time being, (b) You can't find the tangential acceleration with the given information. (c) Tangential acceleration is not zero but insufficient information is given. (d) Tangential acceleration a, = 137/6 m/s? O (a) O (b) O (c) O (d)The apparatus below is a massless wheel of radius that is mounted to a frictionless axle. A small, dense piece of clay with mass is glued to edge of the wheel as shown. Another mass hangs from a massless string that is wrapped around the wheel. We can assume the string is inextensible and does not slip, and the system is in a uniform gravitational field. In terms of the rotation angle of the wheel, write down the total potential energy of the system of both masses. Take note of any constraints that you use to write this as a 1D problem.The torque that a motor develops depends on the rotation rate of its drive shaft according to τ(ω) = 137 - 13ω (N m), where the angular velocity is measured in rad/s. What is the maximum power output of this engine, in W? (Please answer to the fourth decimal place - i.e 14.3225)
- The system is made up of the 1-m, 7.1-kg uniform rod AB and the two uniform disks (each of 0.17 m radius and 1.9 kg mass). If the system is released from rest when = 63°, determine the total external work done to this system when rod AB has just become horizontal. Assume the disks roll without slipping. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point, and proper Sl unit. Take g = 9.81 m/s². B m Ө Your Answer: Answer units BPlease provide the right answer