Conceptual Example 14 provides useful background for this problem. A playground carousel is free to rotate about its center on frictionless bearings, and air resistance is negligible. The carousel itself (without riders) has a moment of inertia of 102 kg·m2. When one person is standing at a distance of 1.42 m from the center, the carousel has an angular velocity of 0.626 rad/s. However, as this person moves inward to a point located 0.520 m from the center, the angular velocity increases to 0.877 rad/s. What is the person's mass?
Suppose the person's mass = M
So, initial moment of inertia of carousel, I1 = 102 kg*m^2 + M*1.42^2
Initial angular velocity, w1 = 0.626 rad/s
Final moment of inertia, I2 = 102 kg*m^2 + M*0.52^2
Final angular velocity, w2 = 0.877 rad/s
Aply conservation of angular momentum -
I1*w1 = I2*w2
=>(102 + M*1.42^2)*0.626 = (102 + M*0.52^2)*0.877
=> 63.85 + 1.26*M = 89.45 + 0.24*M
=> 1.02*M = 25.6
=> M = 25.6/1.02 = 25.10 kg
So, the person's weight = 25.10 kg (Answer)
Conceptual Example 14 provides useful background for this problem. A playground carousel is free to rotate...
Conceptual Example 14 provides useful background for this problem. A playground carousel is free to rotate about its center on frictionless bearings, and air resistance is negligible. The carousel itself (without riders) has a moment of inertia of 134 kg·m2. When one person is standing at a distance of 1.41 m from the center, the carousel has an angular velocity of 0.595 rad/s. However, as this person moves inward to a point located 0.648 m from the center, the angular...
Conceptual Example 13 provides useful background for this problem. A playground carousel is free to rotate about its center on frictionless bearings, and air resistance is negligible. The carousel itself (without riders) has a moment of inertia of 125 kg · m2. When one person is standing on the carousel at a distance of 1.5 m from the center, the carousel has an angular velocity of 0.6 rad/s. However, as this person moves inward to a point located 0.734 m...
Conceptual Example 13 provides useful background for this problem. A playground carousel is free to rotate about its center on frictionless bearings, and air resistance is negligible. The carousel itself (without riders) has a moment of inertia of 125 kg · m2. When one person is standing on the carousel at a distance of 1.5 m from the center, the carousel has an angular velocity of 0.6 rad/s. However, as this person moves inward to a point located 0.973 m from the center, the angular velocity increases to 0.8 rad/s. What is the person's mass?
A playground carousel is free to rotate about its center on frictionless bearings, and air resistance is negligible. The carousel itself (without riders) has a moment of inertia of 125 kg�m2. When one person is standing at a distance of 1.50 m from the center, the carousel has an angular velocity of 0.700 rad/s. However, as this person moves inward to a point located 0.750 m from the center, the angular velocity increases to 0.870 rad/s. What is the person's...
As seen from above, a playground carousel is rotating counterclockwise about its center on frictionless bearings. A person standing still on the ground grabs onto one of the bars on the carousel very close to its outer edge and climbs aboard. Thus, this person begins with an angular speed of zero and ends up with a nonzero angular speed, which means that he underwent a counterclockwise angular acceleration. The carousel has a radius of 1.56 m, an initial angular speed...
1) The parallel axis theorem provides a useful way to calculate the moment of inertia I about an arbitrary axis. The theorem states that I = Icm + Mh2, where Icm is the moment of inertia of the object relative to an axis that passes through the center of mass and is parallel to the axis of interest, M is the total mass of the object, and h is the perpendicular distance between the two axes. Use this theorem and...
Suppose a 55 kg person stands at the edge of a 5.5 m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of 1600 kg·m2. The turntable is at rest initially, but when the person begins running at a speed of 3.4 m/s (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable. (Assume the person is running in the...
Consult Conceptual Example 9 in preparation for this problem. Interactive LearningWare 6.3 also provides useful background. The drawing shows a person who, starting from rest at the top of a cliff, swings down at the end of a rope, releases it, and falls into the water below. There are two paths by which the person can enter the water. Suppose he enters the water at a speed of 15.3 m/s via path 1. How fast is he moving on path...
Problem 10.30 A uniform 2 kg solid disk of radius R = 0.4 m is free to rotate on a frictionless horizontal axle through its center. The disk is initially at rest, and then a 10 g bullet traveling at 500 m/s is fired into it as shown in the figure below. If the bullet embeds itself in the disk at a vertical distance of 0.2 m above the axle, what will be the angular velocity of the disk? Express...
A child pushes her friend (m = 25 kg) located at a radius r = 1.5 m on a merry-go-round (rmgr = 2.0 m, Imgr = 1000 kg*m2) with a constant force F = 90 N applied tangentially to the edge of the merry-go-round (i.e., the force is perpendicular to the radius). The merry-go-round resists spinning with a frictional force of f = 10 N acting at a radius of 1 m and a frictional torque τ = 15 N*m...