(part 1 of 2) A merry-go-round rotates at the rate of 0.12 rev/s with an 83 kg man standing at a point 1.5 m from the axis of rotation. What is the new angular speed when the man walks to a point 0 m from the center? Consider the merry-go-round is a solid 63 kg cylinder of radius of 1.5 m. Answer in units of rad/s. (part 2 of 2) What is the change in kinetic energy due to this movement? Answer in units of J.
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- = (a) In the figure below, wheel A of radius TA B to wheel C of radius rc 10 cm is coupled by belt 25 cm. The angular speed of wheel A is increased from rest at a constant rate of 1.6 rad/s². Find the time needed for wheel C to reach an angular speed of 100 rev/min, assuming the belt does not slip. (Hint: If the belt does not slip, the linear speeds at the two rims must be equal.) TC BIn the figure, wheel A of radiusra = 13.2 cm is coupled by belt B to wheel C of radius rc = 26.2 cm. The angular speed of wheel A is increased from rest at a constant rate of 1.17 rad/s². Find the time needed for wheel C to reach an angular speed of 142 rev/min, assuming the belt does not slip. (Hint: If the belt does not slip, the linear speeds at the two rims must be equal.) B Number i UnitsA horizontal platform in the shape of a circular disk rotates on a frictionless bearing about a vertical axle through the center of the disk. The platform has a radius of 2.36 m and a rotational inertia of 218 kg-m2 about the axis of rotation. A 72.6 kg student walks slowly from the rim of the platform toward the center. If the angular speed of the system is 2.07 rad/s when the student starts at the rim, what is the angular speed when she is 0.433 m from the center? Number i Units
- A merry-go-round has a mass of 1450 kgkg and a radius of 7.50 mm . How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.10 ss ? Assume it is a solid cylinder.A flywheel with a diameter of 1.81 m is rotating at an angular speed of 197 rev/min. (a) What constant angular acceleration (in revolutions per minute-squared) will increase the wheel's angular speed to 929 rev/min in 63.9 s? (b) How many revolutions does the wheel make during that 63.9 s?A child (mass 20 kg) is at the edge of a spinning merry-go-round (approximated as a solid disk of mass 100 kg, radius 2 m). The child walks towards the center of the merry-go-round until he is halfway from the edge. What is the final angular speed of the merry-go-round if the initial angular speed is 10 rad/s?
- A machine part rotates at an angular speed of 0.066 rad/s; its speed is then increased to 2.3 rad/s at an angular acceleration of 0.80 rad/s2. (a) Find the angle through which the part rotates before reaching this final speed. rad (b) If both the initial and final angular speeds are doubled and the angular acceleration remains the same, by what factor is the angular displacement changed? by a factor of 2 by a factor of 4 by a factor of 16 The angular displacement doesn't change.A shaft is turning at 65 rad/s at time t=0. Thereafter, its angular acceleration is given by α = -10 rad/s2 - 5t rad/s3 , where t is the elapsed time. (a) Find its angular speed at t=3 s. (b) How far does it turn in these 3s?A flywheel has a constant angular deceleration of 1.6 rad/s/s. If the flywheel comes to rest from an angular velocity of 269.2 rad/s, what was the angular displacement and the time for the wheel's rotation?
- Energy is to be stored in a 50 kg flywheel in the shape of a uniform solid disk with a radius 1.20m. To prevent structural failure in the flywheel, the maximum allowed radial acceleration of a point on its rim is 3500 m/s2 . What is the maximum kinetic energy that can be stored in the flywheel?A Texas cockroach walks from the center of a circular disk (that rotates like a merry-go-round without external torques) out to the edge at radius R. The angular speed of the cockroach–disk system for the walk is (va = 5.0 rad/s and vb = 6.0 rad/s). After reaching R, what fraction of the rotational inertia of the disk does the cockroach have?A horizontal platform in the shape of a circular disk rotates on a frictionless bearing about a vertical axle through the center of the disk. The platform has a radius of 4.62 m and a rotational inertia of 101 kg-m2 about the axis of rotation. A 66.8 kg student walks slowly from the rim of the platform toward the center. If the angular speed of the system is 2.10 rad/s when the student starts at the rim, what is the angular speed when she is 0.592 m from the center? Number i Units