Consider a rotating disk of radius R and mass M that can rotate about a central axis in horizontal plane. It is initially at rest at t=0. It is given a constant angular acceleration magnitude Z rad/s². Consider a penny of mass m that is placed on the disk at a distan R/2 from the central axis. The coefficient of static friction between the penny and t rotating disk is µ§. At what time will the penny fly off the disk?
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- A particle of mass 0.50 kg starts moves through a circular path in the xy-plane with a position given by r → (t) = (4.0 cos 3t)i ^ + (4.0 sin 3t)j ^ where r is in meters and t is in seconds. (a) Find the velocity and acceleration vectors as functions of time. (b) Show that the acceleration vector always points toward the center of the circle (and thus represents centripetal acceleration). (c) Find the centripetal force vector as a function of time.You are in a carnival ride that consists of a circular room that spins around its center. You stand against the wall at the edge of the room. The room spins at a constant rate of one revolution every 5 seconds, and the room has a radius of 5 m. Your mass is 70 kg. After the room reaches it final speed, the floor drops out from beneath you, yet you remain stuck to the wall. What is the magnitude of the normal force exerted on you by the wall, and at what rate (power) does the normal force perform work on you? (Please explain the power that the normal force does work in detail.)A centrifuge of radius 1.1 m is rotated at 920 revolutionns per minute. What is the force on a partcile of mass 50 g that is positioned midway between the center and edge of the centrifuge.
- A toy aeroplane of mass m = 1,80 kg is attached to a string of length e = 33.0 m and flys in uniform circular motion in a horizontal plane around the centre of its motion. The plane has an engine which generates thrust that keeps the plane moving at a speed of v = 30.7 km/hr. (a) What is the period of the circular motion? Period = S (b) What is the tension in the string holding the aeroplane in its circular motion? Tension = Part 3) A block sits on a sloping plane that can have its angle to the vertical p varied. The angle o initially starts at a value of 90°, and the slope is raised until at an angle o E 33.2° the block starts to slide down the slope. Calculate the coefficient of static friction for this block on this slope.A light, inextensible cord passes over a light, frictionless pulley with a radius of 11 cm. It has a(n) 23 kg mass on the left and a(n) 4 kg mass on the right, both hanging freely. Initially their center of masses are a vertical distance 3.7 m apart. The acceleration of gravity is 9.8 m/s2 . At what rate are the two masses accelerat- ing when they pass each other? Answer in units of m/s2.You are working during your summer break as an amusement park ride operator. The ride you are controlling consists of a large vertical cylinder that spins about its axis fast enough that any person inside is held up against the wall when the floor drops away (Fig. P6.7). The coefficient of static friction between a person of mass mand the wall is us, and the radius of the cylinder is R. You are rotating the ride with an angular speed w suggested by your supervisor. (a) Suppose a very heavy person enters the ride. Do you need to increase the angular speed so that this person will not slide down the wall? (b) Suppose someone enters the ride wearing a very slippery satin workout outfit. In this case, do you need to increase the angular speed so that this person will not slide down the wall?
- In the figure, two blocks, of mass m1 = 257 g and m2 = 337 g, are connected by a massless cord that is wrapped around a uniform disk of mass M = 492 g and radius R = 10.1 cm. The disk can rotate without friction about a fixed horizontal axis through its center; the cord cannot slip on the disk. The system is released from rest. Find (a) the magnitude of the acceleration of the blocks, (b) the tension T1 in the cord at the left and (c) the tension T2 in the cord at the right. M R T2 (a) Number i 0.095238 Units m/s^2 (b) Number Units (c) Number i UnitsA child's top is held in place upright on a frictionless surface. The axle has a radius of r 3.21 mm. Two strings are wrapped around the axle, and the top is set spinning by T T applying T = 2.40 N of constant tension to each string. If it takes 0.590 s for the string to unwind, how much angular 2r momentum L does the top acquire? Assume that the strings do not slip as the tension is applied. R SP 9.15 x10¬3 kg-m² L = S Point P is located on the outer surface of the top, a distance h = 35.0 mm above the ground. The angle that the outer surface of the top makes with the rotation axis of the top is 0 = 24.0°. If the final tangential speed v, of point P is 1.45 m/s, what is the top's moment of inertia I? T 2r T 2.42 x10-4 kg-m? = Incorrect0.1/1E: In the figure, two blocks, of mass m1 = 257 g and m2 = 337 g, are connected by a massless cord that-is wrapped around a uniform disk of mass M = 492 g and radius R = 10.1 cm. The disk can rotate without friction about a fixed horizontal axis through its center; the cord cannot slip on the disk. The system is released from rest. Find (a) the magnitude of the acceleration of the blocks, (b) the tension T in the cord at the left and (c) the tension T2 in the cord at the right. %3D %3! R. (a) Number i Units m/s^2 (b) Number i Units (c) Number Units eTextbook and Media 898 MAY 1 PDF 8 tv .. DD 80 000 000 888 F9 F10 F11 F6 F7 FB F2 F3 F4 F5 @ 23 2$ & 2 3 4 7 8 9
- Please asapConsider a disc of mass 0.44kg, with radius 0.5 m on a slope with angle 45 degrees to the horizontal. It has a good grip on the slope and does not slip. The disc is constructed so that its mass per unit area, ρ(r) = r1/2 kg m−2, with r being the radial distance in metres from the axis of the disc. What is the acceleration of the disc down the slope?Two blocks, which can be modeled as point masses, are connected by a massless string which passes through a hole in a frictionless table. A tube extends out of the hole in the table so that the portion of the string between the hole and M1 remains parallel to the top of the table. The blocks have masses M1 = 1.2 kg and M2 = 2.7 kg. Block 1 is a distance r = 0.55 m from the center of the frictionless surface. Block 2 hangs vertically underneath. 1) If we Assume that block two, M2, does not move relative to the table and that block one, M1, is rotating around the table. What is the speed of block one, M1, in meters per second?