A 170-kg merry-go-round of radius 2.10 m is rotated by pulling a rope that is wrapped around its edge. What is the magnitude of the force (assume it to be constant) on the rope needed to bring the merry- go-round from rest to an angular speed of 0.400 rev/s in 3.00 s? (The moment of inertia of merry-go- round is 1/2MR2).
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- A rock tied to the end of the string swings at a constant angular rate. If you are told that the string can support a total of 100 N of force before breaking, what is the maximum angular velocity the rock can rotate if the rock has a mass of 0.2 kg, and the length of the string is 0.5m? Give your answer in units of radians per second.A 1.3 kg rock is swung in a circular path and in a vertical plane on a 1 m length string. At the top of the path, the angular velocity is 24 rad/s. What is the tension in the string at that point?An astronaut is being tested in a centrifuge. The centrifuge has a radius of 14 m and, in starting, rotates according to 0 = 0.30t2, where t is in seconds and 0 is in radians. (a) When t = 8.0 s, what is the magnitude of the astronaut's angular velocity? rad/s (b) When t = 8.0 s, what is the magnitude of the astronaut's linear speed? m/s (c) When t = 8.0 s, what is the magnitude of the astronaut's tangential acceleration? m/s? (d) When t = 8.0 s, what is the magnitude of the astronaut's radial acceleration? m/s2
- A 40.0-cm diameter disk rotates with a constant angular acceleration of 2.70 rad/s. It starts from rest at t = 0, and a line drawn from the center of the disk to a point P on the rim of the disk makes an angle of 57.3° with the positive x-axis at this time. (a) At t = 2.40 s, find the angular speed of the wheel. rad/s (b) At t = 2.40 s, find the magnitude of the linear velocity and tangential acceleration of P. linear velocity m/s tangential acceleration m/s2 (c) At t = 2.40 s, find the position of P (in degrees, with respect to the positive x-axis). ° counterclockwise from the +x-axisA rock tied to the end of string swings at a constant angular rate. If you are told that the string can support a total of 85 N of force before breaking, what is the maximum angular velocity the rock can rotate if the rock has a mass of 0.16 kg, and the length of the string is 0.5 m? Give your answer in units of radian per secondA race car, starting from rest, travels around a circular turn of radius 28.5 m. At a certain instant, the car is still accelerating, and its angular speed-is 0.794 rad/s. At this time, the total acceleration (centripetal plus tangential) makes an angle of 35.0° with respect to the radius. What is the magnitude of the total acceleration? Number Units
- The propeller of a World War II fighter plane is 2.50 m in diameter. (a) What is its angular velocity in radians per second if it spins at 1100 rev / min? Enter to 3 significant figures W (b) What is the linear speed of its tip at this angular velocity if the plane is stationary on the tarmac? Enter to 3 significant figures V= rad/s (c) What is the centripetal acceleration of the propeller tip under these conditions? Calculate it in meters per second squared Enter to 3 significant figures ac g m/s ac = ✔m/s² Compare the centripetal acceleration to the acceleration due to gravity g. Is the centripetal acceleration very large or very small compared to g? Enter to 3 significant figures = ✓ (d) State what force provided this centripetal acceleration.Riders are seated in a horizontal circle of radius 7.50 m on a carnival ride. They start from rest and accelerate uniformly for 21.0 seconds to a maximum rotational speed of 1.40 rad/s. Calculate the tangential acceleration of the riders during the first 21.0 s of the ride.A point mass of .39kg is set to rotate about a fixed axis .76 m away. The mass is initially at rest and undergoes a constant angular acceleration of 5.10 rad/s^2. At what time will the centripetal force acting on the mass be 50.8N ?
- A flywheel slows from 549.7 rev/min down to 314.7 rev/min while spinning through 40.9 revolutions. What is the angular acceleration of the flywheel (in rad/s/s)? Assume that the flywheel slows down at a constant rate.Human centrifuges are used to train military pilots and astronauts in preparation for high-g maneuvers. A trained, fit person wearing a g-suit can withstand accelerations up to about 9g (88.2 m/s²) without losing consciousness. HINT (a) If a human centrifuge has a radius of 4.54 m, what angular speed (in rad/s) results in a centripetal acceleration of 9g? rad/s (b) What linear speed (in m/s) would a person in the centrifuge have at this acceleration? m/sA 42.0-cm diameter disk rotates with a constant angular acceleration of 3.00 rad/s2. It starts from rest at t = 0, and a line drawn from the center of the disk to a point P on the rim of the disk makes an angle of 57.3° with the positive x-axis at this time. (a) At t = 2.32 s, find the angular speed of the wheel. rad/s (b) At t = 2.32 s, find the magnitude of the linear velocity and tangential acceleration of P. linear velocity m/s tangential acceleration m/s2 (c) At t = 2.32 s, find the position of P (in degrees, with respect to the positive x-axis). _________° counterclockwise from the +x-axis