Identify how many degrees of freedom there are in the following mechanical systems: (a) a compact disc in use (i.e., a rigid body rotating about a fixed axis-all the points in the body that lie along the axis are not moving), (b) a spinning top (i.e., a rigid body rotating about a fixed point - all the points of the body can rotate except for the point on the body that is fixed), (c) a bug crawling on the ground (i.e., a particle moving on a given surface)
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Identify how many degrees of freedom there are in the following mechanical systems: (a) a compact disc in use (i.e., a rigid body rotating about a fixed axis-all the points in the body that lie along the axis are not moving), (b) a spinning top (i.e., a rigid body rotating about a fixed point - all the points of the body can rotate except for the point on the body that is fixed), (c) a bug crawling on the ground (i.e., a particle moving on a given surface)
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- A uniform rod is set up so that it can rotate about an axis at perpendicular to one of its ends. The length and mass of the rod are 0.893 m and 1.19 kg, respectively. A force of constant magnitude F acts on the rod at the end opposite the rotation axis. The direction of the force is perpendicular to both the rod's length and the rotation axis. Calculate the value of F that will accelerate the rod from rest to an angular speed of 6.31 rad/s in 8.87 s. F = NA flywheel is a solid disk that rotates about an axis that is perpendicular to the disk at its center. Rotating flywheels provide a means for storing energy in the form of rotational kinetic energy and are being considered as a possible alternative to batteries in electric cars. The gasoline burned in a 270-mile trip in a typical midsize car produces about 1.64 x 109 J of energy. How fast would a 11.4-kg flywheel with a radius of 0.238 m have to rotate to store this much energy? Give your answer in rev/min.A 34 kg hoop of radius 1.3 m, initially rotating at 301 revolutions per minute, is brought smoothly to a stop in 20 s. What is the average power (in Watts) associated with the force that brings the hoop to a stop?
- An unknown mass is attached via string to the axle (radius 0.20 m) of wheel (radius 0.40 m). The wheel has moment of inertia 0.053 kg•m2. When the system is released from rest, the mass accelerates downward at 0.10 m/s2. What is the mass? How fast is the mass moving if it falls 1.0 m? Hint: use kinematics. What is the total kinetic energy of the system at that location (1.0 m)? What would change if the mass were attached to the wheel instead?An old vinyl record is a thin plastic disk of radius 0.25 m and mass 126 g. It is freely rotating at 45 rev/min. You are able to stop the record from rotating in 6 s by pressing your finer against the rim and exerting a radially directed force of 9 N. (Recommendation: If you don't know what a vinyl record is, please do a Google search for an image to help your understanding.) What is the coefficient of kinetic frictions between the record and your finger??A way to test the tensile strength of a wire is to place a mass at the end of it and spin the mass with uniform circular motion. The speed at which the wire breaks is a measure of its strength. The maximum frequency of rotation before a certain wire breaks is 35.5 Hz. The wire is 50.5 cm long and has a mass of 0.656 kg. (a) Determine the speed with which the mass moves. (b) Calculate the centripetal force acting on the wire
- Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel's energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 1.5 m diameter and a mass of 250 kg. A motor spins up the flywheel with a constant torque of 50N⋅m50N⋅m. How long does it take the flywheel to reach top angular speed of 1200 rpm? Show a diagramA flywheel is a solid disk that rotates about an axis that is perpendicular to the disk at its center. Rotating flywheels provide a means for storing energy in the form of rotational kinetic energy and are being considered as a possible alternative to batteries in electric cars. The gasoline burned in a 131-mile trip in a typical midsize car produces about 3.01 x 10 J of energy. How fast would a 38.5-kg flywheel with a radius of 0.597 m have to rotate to store this much energy? Give your answer in rev/min. Number i jud eTextbook and Media Units >A uniform horizontal disk of radius 5.50 m turns without friction at w = 2.30 rev/s on a vertical axis through its center, as in the figure below. A feedback mechanism senses the angular speed of the disk, and a drive motor at A ensures that the angular speed remain constant while a m = 1.20 kg block on top of the disk slides outward in a radial slot. The block starts at the center of the disk at time t = 0 and moves outward with constant speed v = 1.25 cm/s relative to the disk until it reaches the edge at t = 465 s. The sliding block experiences no friction. Its motion is constrained to have constant radial speed by a brake at B, producing tension in a light string tied to the block. (a) Find the torque as a function of time that the drive motor must provide while the block is sliding. Hint: The torque is given by = 2mrvw. t N-m (b) Find the value of this torque at t= 465 s, just before the sliding block finishes its motion. N.m 2.52 (c) Find the power which the drive motor must…
- A flywheel is a solid disk that rotates about an axis that is perpendicular to the disk at its center. Rotating flywheels provide a means for storing energy in the form of rotational kinetic energy and are being considered as a possible alternative to batteries in electric cars. The gasoline burned in a 187-mile trip in a typical midsize car produces about 2.84 x 109 J of energy. How fast would a 9.42-kg flywheel with a radius of 0.237 m have to rotate to store this much energy? Give your answer in rev/min.Trucks can be run on energy stored in a rotating flywheel, with an electric motor getting the flywheel up to its top speed of 683 rad/s. One such flywheel is a solid, uniform cylinder with a mass of 535 kg and a radius of 1.2 m that rotates about its central axis. What is the kinetic energy of the flywheel after charging? If the truck uses an average power of 8.4 kW, for how many minutes can it operate between chargings?