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 acting at the axle of the merry-go-round, and the merry-go-round is initially at rest. (Hint: Watch the following videos: "Session 9/Lecture/Rotational Motion Example Problems/Net Torque Example Problem 3")
A child (m = 25 kg) is riding on a frictionless merry-go-round at 1.5 m from the center axle. The merry-go-round (Imgr = 1000 kg*m2) is traveling at an angular velocity of 2 rad/s. (Hint: Watch the following videos: "Session 9/Lecture/Rotational Motion Example Problems/HW Problem 1 F-H Hints")
Question for thought: In the process of the child moving outward, is there a torque accelerating the system? If yes, what is the source of the accelerating torque?
A child (m = 25 kg) walks along a 4 m plank of uniform density (m = 8 kg) that is laying with one end extending 1 m off the end of a dock (i.e., 3 m of the plank are on the dock, and 1 m of the plank extends off the dock). (Hint: Watch the following videos: "Session 9/Lecture/Lesson on Rotational Motion/Center of Mass" and "Session 9/Lecture/Rotational Motion Example Problems/Net Torque Example Problem 1" and "Session 9/Lecture/Rotational Motion Example Problems/Net Torque Example Problem 2")
Question for thought: How could the boy test this conclusion without taking the risk of falling in the water?
A person sits on a frictionless stool that is free to rotate but is initially at rest. The person is holding a bicycle wheel (I = 3 kg*m2) that is rotating at 8 rev/s in the clockwise direction as viewed from above, and the moment of inertia of the person-wheel-stool system is 9 kg*m2. For this problem, all answers involving a rotational component will be expressed in revolutions rather than radians. (Hint: Watch the following videos: "Session 9/Lecture/Rotational Motion Example Problems/Conservation of Angular Momentum HW Problem Hints")
Question for thought: (3F) What is the source of the torque that accelerates the student-wheel-stool system?
Concept Question
NOTE: As per Chegg policy Q1 will be answered and only 1st 4 parts of Q1 is answered as it is not been specified in the question which parts need to be answered.
Situation given in question is explained as:
a)What is the magnitude of the torque due to the 90 N force at 2 m?
Torque = r X F
r = 2 m
F = 90 N
both are perpendicular so sin theta between them is 90 and sin 90 = 1
hence magnitude of force = 190 N-m
b) Direction of torque :
Direction of torque is shown above, it is along the axis and towards the sky.
c) What is the magnitude of the torque due to the 10 N force at 1 m?
r = 1 m
F = 10N
angle is 90
Torque = 10 Nm
d) Direction is along the axis but downwards (opposite to the sky)
A child pushes her friend (m = 25 kg) located at a radius r = 1.5...
A person sits on a frictionless stool that is free to rotate but is initially at rest. The person is holding a bicycle wheel (I = 3 kg*m2) that is rotating at 8 rev/s in the clockwise direction as viewed from above, and the moment of inertia of the person-wheel-stool system is 9 kg*m2. For this problem, all answers involving a rotational component will be expressed in revolutions rather than radians. 1. What is direction of the angular momentum of...
12) A 24.5-kg child (momentum of inertia is mR2 )is standing on the outer edge of a horizontal merry-go-round (treat the merry-go-around as solid cylinder, which has moment of inertia of 1/2mR2) about a vertical axis through its center and a radius of 2.50 m. The entire system (including the child) is initially rotating at 0.200 rev/s a) Find the angular velocity if the child moves to a new position 1.25 m from the center of the merry-go-round. b) If...
m v Before After A child with mass m runs with speed v toward a merry go-round that has a moment of inertia I and radius r and jumps onto its rim as shown in the figure above. The merry-go-round is initially at rest. The merry-go-round rotates about its center with no friction. The magnitude of the final angular velocity is w. Which one of the following statements is true? 7.AO The magnitude of the final angular momentum is 2...
26. A 35 kg child is sitting at the edge of a 750 kg merry-go-round (assume it is a solid uniform cylinder or disk) with radius 2.0 m which is rotating once every 30 seconds. a. Calculate the angular velocity of the merry-go-round. 0.21 rad's b. Calculate the speed of the child. 0.42 m/s C. Calculate the angular momentum of the merry-go-round and child together. 343.5 d. If the child moves into the center of the merry-go-round, what will the...
A 50.0 kg child is on a 200.0 kg merry-go-round with a radius of 1.50 m. The child starts at 0.5 m from the center and moves to the edge. The child's parent accelerates the merry-go-round from rest at 0.75Td to a speed of 1.5 Fad How long did the parent push the merry-go-round? How much force is required to hold the child when at 0.5 m from the center? (This centripetal force could be from friction, holding on, or...
A 85 kg person, which tan be treated at a point maw. 11 initially located at the edge of a I SO kg solid merry go round with a radius of 2 meters rotating clockwise at a rate of 0.5 revolutions per second. The then moves toward the center of the merry-go-round to a radius of 1 m Calculate the Initial moment of inertia for the system about the given pivot point Calculate the magnitude and direction of the initial...
A merry-go-round with moment of inertia 400 kg-m^2 and radius 2.0m is rotating with angular speed 0.50 rad/s in the clockwise direction about a fixed axis. A child of mass 40 kg runs tangentially to the merry-go-round with speed 3.0m/s and grabs onto the outside edge of the merry-go-round. a. What is the final angular velocity of the system (merry-go-round plus child)/ What is the final tangential speed of the child? b. What is the change in kinetic energy? c....
6. (25 points) The following question examines the motion of two children on a merry-go- round. You may treat the children as point particles with mass m and the merry-go-round as a disk with mass M and radius R. The moment of inertia of a disk is Idisk MR2 0wn o r Ve n e r (a) Calculate the total energy of the system if the two children are at the edge of the merry- go-round and the merry-go-round is...
A merry-go-round modeled as a disk of mass 100 kg and radius 2.0 m is rotating around a frictionless vertical axle. After a person of mass 60 kg jumps onto the merry-go-round, the system’s angular speed decreases to 2.0 rad/s. If the person walks slowly from the edge toward the center, find the change in the system’s rotational kinetic energy caused by her movement to 0.5 m from the center.
A playground merry-go-round has a radius of R = 4.0m and has a moment of inertia I_cm = 7.0 times 10^3 kg middot m^2 about an axis passing through the center of mass. There is negligible friction about its vertical axis. Two children each of mass m = 25kg are standing on opposite sides a distance r_0 = 3.0m from the central axis. The merry-go-round is initially at rest. A person on the ground applies a constant tangential force of...