A stationary bicycle is raised off the ground, and its front wheel (m = 1.3 kg) is rotating at an angular velocity of 14.4 rad/s (see the drawing). The front brake is then applied for 3.0 s, and the wheel slows down to 2.1 rad/s. Assume that all the mass of the wheel is concentrated in the rim, the radius of which is 0.34 m. The coefficient of kinetic friction between each brake pad and the rim is
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- A potter's wheel having a radius 0.52 m and a moment of inertia of 11.3 kg · m2 is rotating freely at 53 rev/min. The potter can stop the wheel in 6.0 s by pressing a wet rag against the rim and exerting a radially inward force of 68 N. Find the effective coefficient of kinetic friction between the wheel and the wet rag.One end of a cord is fixed and a small 0.700-kg object is attached to the other end, where it swings in a section of a vertical circle of radius 2.50 m, as shown in the figure below. When 8 = 30.0°, the speed of the object is 8.50 m/s. (a) At this instant, find the magnitude of the tension in the string. N (b) At this instant, find the tangential and radial components of acceleration. at = m/s² downward tangent to the circle m/s² inward a = (c) At this instant, find the total acceleration. inward and below the cord at (d) Is your answer changed if the object is swinging down toward its lowest point instead of swinging up? O Yes O No (e) Explain your answer to part (d).A coin rests 14.5 cm from the center of a turntable. The coefficient of static friction between the coin and turntable surface is 0.310. The turntable starts from rest at t = 0 and rotates with a constant angular acceleration of 0.640 rad/s2. (a) Once the turntable starts to rotate, what force causes the centripetal acceleration when the coin is stationary relative to the turntable? Under what condition does the coin begin to move relative to the turntable? (b) After what period of time will the coin start to slip on the turntable? s
- A horizontal merry-go-round is initially at rest. At t = 0, it is given a constant angular acceleration ? = 0.0710 rad/s2, which increases its angular velocity. A 23.5 kg child sits at 2.35 m from the axis of rotation. (a) At t = 9.70 s, determine the centripetal force acting on the child. ________ N (b) At t = 9.70 s, determine the direction of the net force acting on the child. Specify the angle from the radially inward direction. ________ ° (c) Through how many radians has the merry-go-round rotated within that 9.70 s time? _______ radA yo-yo has a rotational inertia of 950 g cm2 and a mass of 120 g. Its axle radius is 3.2 mm, and its string is 120 cm long. The yo-yo rolls from rest down to the end of the string. (a)What is the magnitude of its linear acceleration? (b) How long does it take to reach the end of the string? As it reaches the end of the string, what are its (c) linear speed, (d) translational kinetic energy, (e) rotational kinetic energy, and (f) angular speed?You have a grindstone (a disk) that is 77.0 kg, has a 0.400-m radius, and is turning at 89.0 rpm, and you press a steel axe against it with a radial force of 16.0 N. (a)Assuming the kinetic coefficient of friction between steel and stone is 0.50, calculate the angular acceleration (in rad/s2) of the grindstone. (Indicate the direction with the sign of your answer.) rad/s2 (b)How many turns (in rev) will the stone make before coming to rest? rev
- A car initially traveling at 24.7 m/s undergoes a constant negative acceleration of magnitude 1.80 m/s2 after its brakes are applied. (a) How many revolutions does each tire make before the car comes to a stop, assuming the car does not skid and the tires have radii of 0.340 m? rev (b) What is the angular speed of the wheels when the car has traveled half the total distance? rad/sA stationary bicycle is raised off the ground, and it's front-wheel (m= 2.83 kg) is rotating at an angular velocity of 16.5 rad/s ( see the figure). The front brake is then applied for 3.18s and the wheel slows down to 3.86 rad/s. Assume that all the masses of the wheel is concentrated in the rim, the radius of which is 0.330 m. The coefficient of kinetic friction between each brake and pad and the rim is Uk = 1.26. What is the magnitude of the normal force that each brake pad applies to the rim?An old vinyl record is a thin plastic disk of radius 0.25 m and mass 126 g. It is freely rotating at 45 rev/min. You are able to stop the record from rotating in 6 s by pressing your finer against the rim and exerting a radially directed force of 9 N. (Recommendation: If you don't know what a vinyl record is, please do a Google search for an image to help your understanding.) What is the coefficient of kinetic frictions between the record and your finger??
- A way to test the tensile strength of a wire is to place a mass at the end of it and spin the mass with uniform circular motion. The speed at which the wire breaks is a measure of its strength. The maximum frequency of rotation before a certain wire breaks is 35.5 Hz. The wire is 50.5 cm long and has a mass of 0.656 kg. (a) Determine the speed with which the mass moves. (b) Calculate the centripetal force acting on the wireA potter's wheel having a radius 0.48 m and a moment of inertia of 10.5 kg · m2 is rotating freely at 50 rev/min. The potter can stop the wheel in 4.0 s by pressing a wet rag against the rim and exerting a radially inward force of 69 N. Find the effective coefficient of kinetic friction between the wheel and the wet rag.A car initially traveling at 28.7 m/s undergoes a constant negative acceleration of magnitude 2.00 m/s2 after its brakes are applied. (a) How many revolutions does each tire make before the car comes to a stop, assuming the car does not skid and the tires have radii of 0.350 m? rev (b) What is the angular speed of the wheels when the car has traveled half the total distance? rad/s