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A solid sphere and a solid cylinder (both have mass M and radius R) are released from rest at the top of an inclined plane of height H that makes an angle θ with the horizontal (see figure 7).
a) Assume that both roll without slipping, find the time taken by the sphere and the cylinder to reach the bottom. Which object wins the race?
b) What should the value of the angle θ be such that both the sphere and cylinder are able to roll down the incline without slipping?
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- A 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.A solid sphere, a solid cylinder, a hollow cylinder, and an unopened can of soda, all of the same mass m and the same outer radius R, are released from rest at the top of an incline and start rolling without sliding. In which place will the can finish? third fourth second firstA spherical shell of radius 3.09 cm and a sphere of radius 7.47 cm are rolling without slipping along the same floor. The two objects have the same mass. If they are to have the same total kinetic energy, what should the ratio of the spherical shell's angular speed to the sphere's angular speed be?
- A solid sphere, a spherical shell, a hoop, and a disk all with mass M and radius R roll without slipping with the same speed along a flat surface. They then start to roll up a slope that makes and angle θ with respect to the horizontal. Which object gets the farthest up the slope before rolling back down?Thank you for your help in understanding the concepts on how to work out these types of practice problems.A solid cylinder with radius, R, mass, M and length, L is fixed to rotate on its cylindrical axis. A string with negligible mass wound around the cylinder and pulled with force, F. What is the linear acceleration of a point on the outer circumference of the cylinder?
- 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 robot wheel rotates with a constant angular speed of 3.8 rad/s. The radius of the robot wheel is radius = 0.4 meters. Find the following: a) angular displacement of the robot wheel at a time of 7 seconds. b) linear (tangential) speed of a point on the rim.A m = 2kg ring has a radius of r = 0.5m. The moment of inertia of a ring is I = m r². The ring has an initial speed of v= 1 m/s on the horizontal surface. It rolls, without slipping, along the surface and up the ramp, where it stops when it reaches a height h. a) What is the angular velocity of the ring when it is on the horizontal surface? v=1m/s b) While the ring is on the horizontal surface, what is the speed of a point at the top of the ring? c) Use Conservation of Energy to find the maximum height of the ring, h. Show all your work. Solve the problem using variables. Only substitute numbers in the very last step. d) How would the maximum height change in each of the following situations? Put an X in the correct answer for each statement. The ring has a larger mass m (same r and v) The ring is replaced with a solid disc (same m, r, and v) There is no friction and the ring slides instead of rolling (same m, r, and v) Higher v=0 Lower Same height h
- A uniform sphere is placed inside hemispherical bowl of radius R = 75.0 cm. It is released from rest at an angle 0 = 40.0°. What is the speed of the sphere at the bottom of the bowl if it rolls without slipping? Ishpere = 2/5 mr². Assume r<Modern wind turbines generate electricity from wind power. The large, massive blades have a large moment of inertia and carry a great amount of angular momentum when rotating. A wind turbine has a total of 3 blades. Each blade has a mass of m = 5500 kg distributed uniformly along its length and extends a distance r = 44 m from the center of rotation. The turbine rotates with a frequency of f = 12 rpm. a)Calculate the total moment of inertia of the wind turbine about its axis, in units of kilogram meters squared. b)Enter an expression for the angular momentum of the wind turbine, in terms of the defined quantities. c)Calculate the angular momentum of the wind turbine, in units of kilogram meters squared per second.A uniform solid ball rolls without slipping down a plane which is inclined at 31° to the horizontal. If the ball has a radius r=0.4m, a mass m=0.1 kg and starts from rest, find: a) the speed of the ball after it travels 2m down the incline. b) at this point, what is the angular momentum of the ball? c) If the coefficient of friction between the ball and the plane is 0.25, what is the maximum angle of inclination that allows the ball to roll without slipping?SEE MORE QUESTIONS