One end of a string 1 m long is fixed and a body of mass 500 grams is tied to the other end. If breaking tension is 98 N, find the maximum angular velocity of the body that the string can withstand when rotated in horizontal circle.
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- A solid, uniform disk of radius 0.250 m and mass 57.8 kg rolls down a ramp of length 4.70 m that makes an angle of 16.0° with the horizontal. The disk starts from rest from the top of the ramp. (a) Find the speed of the disk's center of mass when it reaches the bottom of the ramp. m/s (b) Find the angular speed of the disk at the bottom of the ramp. rad/sA compact disk of diameter 8 cm starts from rest and speeds up uniformly to 2 rev/s in 4.0 seconds. What is the tangential acceleration of a point on the outer rim of the disk moving at 3 rev/s?The force of T = 23 N is applied to the cord of negligible mass. Determine the angular velocity of the 20-kg wheel when it has rotated 2.9 revolutions starting from rest. The wheel has a radius of gyration of ko = 0.2 m.
- Consider the 12.0 kg motorcycle wheel shown in the figure. Assume it to be approximately an annular ring with an inner radius of R₁ = 0.280 m and an outer radius of R₂ = 0.480 m. The motorcycle is on its center stand, so that the wheel can spin freely. R₁ (a) If the drive chain exerts a force of 1825 N at a radius of 5.00 cm, what is the angular acceleration of the wheel in rad/s²? rad/s2 (b) What is the tangential acceleration, in m/s², of a point on the outer edge of the tire? m/s² (c) How long in seconds, starting from rest, does it take to reach an angular velocity of 80.0 rad/s?A solid, uniform disk of radius 0.250 m and mass 61.2 kg rolls down a ramp of length 5.10 m that makes an angle of 18.0° with the horizontal. The disk starts from rest from the top of the ramp. (a) Find the speed of the disk's center of mass when it reaches the bottom of the ramp. |m/s (b) Find the angular speed of the disk at the bottom of the ramp. rad/sA compact disc (CD) contains music on a spiral track. Music is put onto a CD with the assumption that, during playback, the music will be detected at a constant tangential speed at any point. Since vT = r, a CD rotates at a smaller angular speed for music near the outer edge and a larger angular speed for music near the inner part of the disc. For music at the outer edge (r = 0.0568 m), the angular speed is 4.44 rev/s. Find (a) the constant tangential speed at which music is detected and (b) the angular speed (in rev/s) for music at a distance of 0.0449 m from the center of a CD.
- An automobile traveling 58.0 km/h has tires of 71.0 cm diameter. (a) What is the angular speed of the tires about their axles? (b) If the car is brought to a stop uniformly in 37.0 complete turns of the tires, what is the magnitude of the angular acceleration of the wheels? (c) How far does the car move during the braking? (Note: automobile moves without sliding)A person with an axe to grind is using a whetstone. The whetstone is connected to a motor which keeps it rotating at 85 rev/min. The whetstone is a solid cylinder of made of a special type of stone of mass 45 kg and radius 20 cm. The heavy axeblade is being pressed onto the whetstone with a steady force of 25 N directed into the centre of the whetstone. Suddenly, the power to the motor is cut but the person maintains the force of the axe on the whetstone. The coefficient of kinetic friction between the axe and the stone is 0.60. The moment of inertia of a cylinder about it's centre of mass is I = ½MR2. (a) Calculate the torque of the frictional force on the wheel. (b) Calculate the total angle through which the wheel turns from the time the power goes off to the time the whetstone stops rotating. (c) How long does it take for the wheel to stop after the power outage?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 uniform, solid sphere of radius 6.00 cm and mass 4.50 kg starts with a purely translational speed of 2.50 m/s at the top of an inclined plane. The surface of the incline is 2.00 m long, and is tilted at an angle of 32.0∘ with respect to the horizontal. Assuming the sphere rolls without slipping down the incline, calculate the sphere's final translational speed v2 at the bottom of the ramp. v2= m/sA solid, uniform disk of radius 0.250 m and mass 49.0 kg rolls down a ramp of length 3.80 m that makes an angle of 12.0° with the horizontal. The disk starts from rest from the top of the ramp. (a) Find the speed of the disk's center of mass when it reaches the bottom of the ramp. m/s (b) Find the angular speed of the disk at the bottom of the ramp. rad/s