A 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 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.

Similar questions

A Texas cockroach of mass 0.246 kg runs counterclockwise around the rim of a lazy Susan (a circular disk mounted on a vertical axle) that has a radius 18.0 cm, rotational inertia 3.36 x 10³ kg-m?, and frictionless bearings. The cockroach's speed (relative to the ground) is 2.75 m/s, and the lazy Susan turns clockwise with angular velocity wo = 3.31 rad/s. The cockroach finds a bread crumb on the rim and, of course, stops. (a) What is the angular speed of the lazy Susan after the cockroach stops? (b) Is mechanical energy conserved as it stops? (a) Number Units (b)
An electric motor rotating a workshop grinding wheel at 1.08 x 10 rev/min is switched off. Assume the wheel has a constant negative angular acceleration of magnitude 2.06 rad/s? (a) How long does it take the grinding wheel to stop? Note that the time required for the wheel to stop is the same as the time for the wheel to start from rest and reach the given angular speed with the same magnitude angular acceleration, s (b) Through how many radians has the wheel turned during the time interval found in part (a)? It might be helpful to translate this problems into linear variables (a car traveling with an initial speed and then slowing down with a constant negative acceleration), rad Need Help? Road Master
Someone frequently throws a tennis ball for their dog to chase.Throughout the throwing motion, the angular velocity of their arm is 6.7radians/s, and the radius of rotation of the ball is 63.0 cm.One day they decide to test out a ball-throwing tool which effectivelyextends the radius of rotation by an extra 36 cm. Assuming all othervariables are equal, how much faster (in m/s) can they throw the ballwhen they use the launcher compared to when they don't?Express your answer to 2 decimals, and don't include units+. Please type answer not write by hend
In the figure, wheel A of radius -9.40 cm is coupled by belt B to wheel C of radius rc-26.1 cm. The angular speed of wheel A is increased from rest at a constant rate of 2.53 rad/s². Find the time needed for wheel C to reach an angular speed of 63.0 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.) Number Ma Units B
NASA physicians need to know whether the contents of astronauts' skulls (brain, eyes, eardrums, etc.) move so much during rotational maneuvers that injury might be caused. If you are an astronaut in a spinning spacecraft and have an initial angular displacement of 3.14 radians, an initial angular velocity of 3.683 radians per second, and an angular acceleration of 0.02 radians per second squared, what distance will your eyes have traveled around the center of your skull after 26.83 seconds?
A uniform disk (1=1/2 mR2) has a mass of 3 kg and a radius of 2m. The disk is mounted on frictionless bearings and is used as a turntable. The turntable is initially rotating at 120 rpm (revolutions per minute, convert it to rad/s). A hollow cylinder has the same mass and radius as the disk. It is released from rest, just above the turntable, and on the same vertical axis. The hollow cylinder slips on the turntable for 0.20 s until it acquires the same final angular velocity as the turntable. (HINT: Note that some of the information given is not needed! Think which conservation law(s) apply.) The final angular momentum of the system is closest to: L = Submit [5] ΑΣΦ Request Answer ? kg. m²/s 4
A ceiling fan can accelerate from rest to 2pi rad/s in 8 seconds. (A) what is the angular acceleration of the fan? (B) find the angular displacement of the fan during the first 5 seconds. (C) at the full angular speed of 2pi rad/s find the corresponding tangential speed of a point at the rim of the wing if the radius of the wing is r=0.5m. (D) what is the centripetal acceleration of a point at the rim (r=0.5 m) when the fan reaches full speed? can you give detailed steps please?
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, and (d) the number of revolutions from rest until the time the disk reaches the 10 rev/s angular speed.
A 0.45 kg tetherball is attached to a pole and rotating in a horizontal circle of radius r₁ = 1.4 m and is circling at angular speed = 1.42 rad/s. As the rope wraps around the pole the radius of the circle shortens and became r2 = 0.9 m, that decreases the moment of inertia of the rotating tetherball. Neglecting air resistance what will be the angular speed of the ball after the rope is wrapped around the pole measured in kgm2/s (answer with 3 decimal places)? A
A dragster starts from rest and accelerates down a track. Each tire has a radius of 0.320 m and rolls without slipping. At a distance of 393 m, the angular speed of the wheels is 253 rad/s. Determine (a) the linear speed of the dragster and (b) the magnitude of the angular acceleration of its wheels.