A wheel is rotating clockwise as shown (by the arrow). Its rotation axis coincides with the x-axis. A torque that causes the wheel to slow down is best represented by the vector 1 O 2 O 3 4 21 5
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- A 20-kg child running at 1.4 m/s jumps onto a playground merry-go-round that has mass 180 kg and radius 1.6m. She is moving tangent to the platform when she jumps and she lands right on the edge. What is the angular velocity of the child and the merry-go-round if the merry-go-round started from rest? You can treat the merry-go-round as a solid disc and ignore any friction in its axle. Please answer in units of rad/sec.A kid runs towards the edge of a merry-go-round that is not rotating and jumps on. The merry-go-round then rotates with a constant angular velocity ω. Assume that the kid has a mass of 40 kg and is initially running at a speed of 2 m/s tangent to the edge of the merry-go-round. The merry-go-round is a uniform disk with a mass of 120 kg and a radius of 2 m. Assume that it rotates without friction. What is the final angular velocity ωf (in radians/s) of the merry-go-round (with the kid riding)? Please write out steps, not type-I have dyslexiaA kid runs towards the edge of a merry-go-round that is not rotating and jumps on. The merry-go-round then rotates with a constant angular velocity ω. Assume that the kid has a mass of 40 kg and is initially running at a speed of 4 m/s tangent to the edge of the merry-go-round. The merry-go-round is a uniform disk with a mass of 80 kg and a radius of 2 m. Assume that it rotates without friction. What is the final angular velocity ωf (in radians/s) of the merry-go-round (with the kid riding)?
- 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?You are riding your bicycle down the road and decide to stop to take in the scenery. Initially, your bicycle tires are rotating at a frequency of 7 times per second. If it takes your bicycle 50 revolutions to come to a full stop, what is the magnitude of the angular acceleration (assume your acceleration is constant). Give your answer in units of radians per second squaredConsider a phonograph with a diameter of 0.6 m and a rotational speed of 33 RPM. Answer the following questions. What is its radius in m?What is its rotational speed in rad/s?What is the tangential speed on the phonograph's outer edge in m/s?What is the tangential speed at the center of the phonograph in m/s?What is the tangential speed halfway out to the edge of the phonograph?
- A uniform horizontal disk of radius 5.50 m turns without friction at w = 2.30 rev/s on a vertical axis through its center, as in the figure below. A feedback mechanism senses the angular speed of the disk, and a drive motor at A ensures that the angular speed remain constant while a m = 1.20 kg block on top of the disk slides outward in a radial slot. The block starts at the center of the disk at time t = 0 and moves outward with constant speed v = 1.25 cm/s relative to the disk until it reaches the edge at t = 465 s. The sliding block experiences no friction. Its motion is constrained to have constant radial speed by a brake at B, producing tension in a light string tied to the block. (a) Find the torque as a function of time that the drive motor must provide while the block is sliding. Hint: The torque is given by = 2mrvw. t N-m (b) Find the value of this torque at t= 465 s, just before the sliding block finishes its motion. N.m 2.52 (c) Find the power which the drive motor must…The earth spins on its axis once a day and orbits the sun once a year (360 days !!!). In each case take the positive direction for the angular displacement to be the direction of the earth's motion. Determine its angular velocity as it revolves around the sun.What is the angle between the vectors a = (10, -10, 0) and b = (-5, 5, 2), in radians?