A hollow cylinder of mass M1 and radius R1 rolls without slipping on the inside surface of another hollow cylinder of mass M2 and radius R2. Assume R1<
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A hollow cylinder of mass M1 and radius R1 rolls without slipping on the inside surface of another hollow cylinder of mass M2 and radius R2. Assume R1<<RZ. Both axes are horizontal, and the larger cylinder is free to rotate about its axis What is the
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- A disk 8.08 cm in radius rotates at a constant rate of 1 250 rev/min about its central axis. (a) Determine its angular speed. rad/s(b) Determine the tangential speed at a point 2.96 cm from its center. m/s(c) Determine the radial acceleration of a point on the rim. magnitude direction (d) Determine the total distance a point on the rim moves in 2.04 s.Chapter 15, Problem 039 The balance wheel of a watch oscillates with angular amplitude 0.64n rad and period 0.68 s. Find (a) the maximum angular speed of the wheel, (b) the angular speed of the wheel at displacement 0.64n/2 rad, and (c) the magnitude of the angular acceleration at displacement 0.64n,/4 rad. (a) Number Units (b) Number Units (c) Number UnitsA uniform rigid rod initially at rest has length L = 100 cm and mass MR = 0.500 kg. The rod hangs vertically and is pivoted at its upper end. A ball of mass MB = 4.00 kg is attached to the lower end of the rod. See figure. The pivot is frictionless. What minimum horizontal speed must be imparted to the ball in order for the ball to go over the top of the vertical circle?
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- A wheel is rotating clockwise on a fixed axis perpendicular to the page (x). A torque that causes the wheel to slow down is best represented by the vector Z! 2 te 110*12-168. A particle travels along the portion of the "four- leaf rose" defined by the equation r= (5 cos 20) m. If the angular velocity of the radial coordinate line is 0=(31²) rad/s, where t is in seconds, determine the radial and transverse components of the particle's velocity and acceleration at the instant = 30°. When t=0,0=0. ① r = (5 cos 20) Prob. 12-168= (a) In the figure below, wheel A of radius TA B to wheel C of radius rc 10 cm is coupled by belt 25 cm. The angular speed of wheel A is increased from rest at a constant rate of 1.6 rad/s². Find the time needed for wheel C to reach an angular speed of 100 rev/min, assuming the belt does not slip. (Hint: If the belt does not slip, the linear speeds at the two rims must be equal.) TC B
- A thin circular hoop of mass 1.0 ?? and radius 2.0 ? is rotating about an axis through its center and perpendicular to its plane. It is slowing down at the rate of 7.0 ???/?2. The net torque acting on it isA mass m=10kg is fastened to a light spring k=380N/m by a light that passes over a pulley. Assume the pulley is a uniform cylinder of mass Mp=5kg and radius R=0.2m and rotates without friction. The mass is released from rest when the spring is unstretched. The spring remains firmly fixed to the floor and to the string. What is the angular velocity of the pulley when the mass has fallen a distance h=0.4m stretching the spring.A playground carousel is rotating counterclockwise about its center on frictionless bearings. A person standing still on the ground grabs onto one of the bars on the carousel very close to its outer edge and climbs aboard. Thus, this person begins with an angular speed of zero and ends up with a nonzero angular speed, which means that he underwent a counterclockwise angular acceleration. The carousel has a radius of 1.62 m, an initial angular speed of 3.21 rad/s, and a moment of inertia of 128 kg·m2. The mass of the person is 41.9 kg. Find the final angular speed of the carousel after the person climbs aboard.