(a) Deduce an expression for a rotation operation along z-axis
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- Unless otherwise stated, assume the density is constantThe disk of a rotating cutter rotates about its central axis at 33.5 rev/min and takes 60 seconds to come to rest when switched off. Calculate, Its angular acceleration α The number of revolutions it makes before coming to restthe slender bar of length l and mass m is pinned to verical shaft at O, the vertical shaft rotates with a cnstant angular velocity w0, please find the value of necessary for the bar to remain at a constant angular β relative to the verical
- A solid sphere of mass M and radius R rolls without slipping down a rough incline that makes an angle θ with the horizontal. Find the magnitude of the linear acceleration a of the sphere.A solid sphere with a mass of 1.0 kg and radius of 10 cm rolls down an inclined plane that is 1.0 m long andat an angle of 26◦ from the horizontal. The sphere is released from rest at the top of the plane, and it rollsdown to the bottom where it continues to roll along a horizontal surface.(a) What is the rotational speed of the sphere at the bottom of the plane?(b) What is the angular momentum of the sphere at the bottom of the plane?(c) How many revolutions does the sphere make if it rolls along the horizontal surface for 25 s before comingto a stop?Hint: you can assume the acceleration of the sphere along the horizontal surface is constant.Can you help me with this physics question? A force vector (2, -1, 4)N acts on a particle at the position (1, -3, 0)m. What is the torque due to this force about the origin?
- A box of mass m,=9.4 kg on a rough inclined plane of angle a= 58° is connected with a string of negligible mass over a pulley 1 z" pulley R to a bucket of mass m,=1 kg. The coefficient of kinetic friction in shape of a disk with a moment of inertia/= between the block and the surface of the incline is u, = 0.19. The mass m, is sliding downward as shown in the figure with a m magnitude of the acceleration of a =0.7 m, m2 1. Calculate the tension in the string T, = N 2. Calculate the tension in the string T2 = 3. Calculate the mass of the pulley m pulley kg Check Finish atA small 4-lb collar C can slide freely on a thin ring of weight 6 lb and radius 10 in. The ring is welded to a short vertical shaft, which can rotate freely in a fixed bearing. Initially, the ring has an angular velocity of 35 rad/s and the collar is at the top of the ring (0 = 0) when it is given a slight nudge. Neglecting the effect of friction, determine (a) the angular velocity of the ring as the collar passes through the position 0 = 90°, (b) the corresponding velocity of the collar relative to the ring.A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is rotating at 10 rev/s; 60 revolutions later, its angular speed is 15 rev/s. Calculate (a) the angular acceleration (b) the time required to complete the 60 revolutions (c) the time required to reach the 10 rev/s angular speed (d) the number of revolutions from rest until the time the disk reaches the 10 rev/s angular speed
- Star Trillian-2009 was initially observed by astronomers to spin with a period of 25 days, and was computed to have a rotational inertia of 23.81 IARIU (International Astronomical Rotational Inertia Units). It then undergoes a change, and the new rotational inertia is calculated to be a third of the original value. What is the new rotational period of the star?In the figure below, the disk, of mass 440 g and radius 3.5 cm, is rotating at 180 rpm on a frictionless shaft of negligible radius. The upper disk, of mass 270 g and radius 2.3 cm, is initially not rotating. It drops freely down onto the lower dis, and frictional forces bring the two disk to a common rotational speed. Find (a) that common speed and (b) the fraction of the initial kinetic energy lost to friction.A winch with a drum of radius R pulls a block at constant speed up a rough incline. The winch is attached to the block with a lightweight, thin cable that runs over a massless roller pulley that turns without friction, as shown. The mass of the block is M, the coefficient of kinetic friction between the block and the incline is μ, and the angle of the incline is 0. Let g denote the acceleration due to gravity. Derive an algberaic expression for the power P supplied by the winch if the winch turns through a total angular displacement during a time interval At. P =