A wheel with radius 0.0600 m rotates about a horizontal frictionless axle at its center. The moment of inertia of the wheel about the axle is 2.50 kg . m2. The wheel is initially at rest. Then at t = 0 a force F = (5.00 N/s)t is applied tangentially to the wheel and the wheel starts to rotate. What is the magnitude of the force at the instant when the wheel has turned through 8.00 revolutions?
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A wheel with radius 0.0600 m rotates about a horizontal
frictionless axle at its center. The moment of inertia of the wheel about
the axle is 2.50 kg . m2. The wheel is initially at rest. Then at t = 0 a
force F = (5.00 N/s)t is applied tangentially to the wheel and the wheel
starts to rotate. What is the magnitude of the force at the instant when
the wheel has turned through 8.00 revolutions?
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- A student holds a bike wheel and starts it spinning with an initial angular speed of 9.0rotations per second. The wheel is subject to some friction, so it gradually slows down. In the 10 s period following the inital spin, the bike wheel undergoes 70 complete rotations. Assuming the frictional torque remains constant, how much more time Δts will it take the bike wheel to come to a complete stop? The bike wheel has a mass of 0.625 kg and a radius of 0.315 m. If all the mass of the wheel is assumed to be located on the rim, find the magnitude of the frictional torque τf that was acting on the spinning wheel.A circular disk with a radius of 0.38 m is subject to 2 tangentially applied forces. The disc is fixed such that it will rotate about its center. Both forces produce a torque in the same direction. The mass of the disc is 0.73 kg. The moment of inertia of a disc is I =1/2MR^2 F1 = 2.3 N applied at the outer edge of the disc. F2 = 3.6 N applied at a distance of 0.29 from the center of the disc. What is the angular acceleration of the disc?A playground merry-go-round of radius R = 1.80 m has a moment of inertia of 1 = 290 kgm² and is rotating at 14.0 rev/min about a frictionless vertical axis. Facing the axle, a 29.0 kg child hops on to the merry-go-round and manages to sit down on its edge. What is the new angular speed of the merry-go-round? O 1.11 rad/s 0.903 rad/s O 10.6 rad/s O4.53 rad/s practice q# 2 p. 242 chap 7
- A small 0.340-kg object moves on a frictionless horizontal table in a circular path of radius 1.10 m. The angular speed is 7.09 rad/s. The object is attached to a string of negligible mass that passes through a small hole in the table at the center of the circle. Someone under the table begins to pull the string downward to make the circle smaller. If the string will tolerate a tension of no more than 108 N, what is the radius of the smallest possible circle on which the object can move? Number UnitsA carousel has a radius of 1.60 m and a moment of inertia of 130 kg · m2. A girl of mass 43.0 kg is standing at the edge of the carousel, which is rotating with an angular speed of 3.10 rad/s. Now the girl walks toward the center of the carousel and stops at a certain distance from the center d. The angular speed of the carousel is now 5.4 rad/s. How far from the center, in meters, did the girl stop? The answer is NOT 1.21mA cylinder with rotational inertia I1 = 3.4 kg · m2 rotates clockwise about a vertical axis through its center with angular speed ?1 = 5.4 rad/s.A second cylinder with rotational inertia I2 = 1.1 kg · m2rotates counterclockwise about the same axis with angular speed ?2 = 7.0 rad/s. If the cylinders couple so they have the same rotational axis, what is the angular speed of the combination (in rad/s)? What percentage of the original kinetic energy is lost to friction?
- A student holds a bike wheel and starts it spinning with an initial angular speed of 9.09.0 rotations per second. The wheel is subject to some friction, so it gradually slows down. In the 10.0 s10.0 s period following the inital spin, the bike wheel undergoes 65.065.0 complete rotations. Assuming the frictional torque remains constant, how much more time Δ?sΔts will it take the bike wheel to come to a complete stop? Δ?s=Δts= ss The bike wheel has a mass of 0.725 kg0.725 kg and a radius of 0.385 m0.385 m. If all the mass of the wheel is assumed to be located on the rim, find the magnitude of the frictional torque ?fτf that was acting on the spinning wheel.A very light rope is wrapped around a wheel of radius R = 2.0 meters and does not slip. The wheel is mounted with frictionless bearings on an axle through its center. A block of mass 14 kg is suspended from the end of the rope. When the system is released from rest it is observed that the block descends 10 meters in 2.0 seconds. What is the moment of inertia of the wheel?A circular disk with a radius of 0.5 m is subject to 2 tangentially applied forces. The disc is fixed such that it will rotate about its center. Both forces produce a torque in the same direction. The mass of the disc is 0.69 kg. The moment of inertia of a disc is I MR² = F₁ = 2.6 N applied at the outer edge of the disc. F₂ = 4 N applied at a distance of 0.26 from the center of the disc. What is the angular acceleration of the disc?
- A carousel has a radius of 1.60 m and a moment of inertia of 130 kg · m2.A girl of mass 43.0 kg is standing at the edge of the carousel, which is rotating with an angular speed of 3.10 rad/s. Now the girl walks toward the center of the carousel and stops at a certain distance from the center d. The angular speed of the carousel is now 5.4 rad/s. How far from the center, in meters, did the girl stop?The string is massless. The pulley turns on frictionless bearings. Moment of Inertia of the pulley about its axis is 0.0125 kg.m2, its radiusR= 10.0 cm. The mass m1= 5.00 kg, and the mass m2= 4.00 kg. The system is released from rest. Find (a) the acceleration of m1 and (b) the tensions, T1& T2, in the horizontal and vertical portions of the string. The horizontal surface below m1 is smooth.A bicycle wheel is mounted on a fixed, frictionless axle, with a light string wound around its rim. The wheel has moment of inertia I=kmr2I=kmr2, where mm is its mass, rr is its radius, and kk is a dimensionless constant between zero and one. The wheel is rotating counterclockwise with angular speed ω0ω0 t=0t=0 someone starts pulling the string with a force of magnitude FF A. Suppose that after a certain time tLtL LL ωfinalωfinal of the wheel? Express your answer in terms of LL FF II ω0ω0 B. What is the instantaneous power PP delivered to the wheel via the force F⃗F→ at time t=0t=0? Express the power in terms of some or all of the variables given in the problem introduction.