(a)
Angular speed of each child.
(a)
Answer to Problem 36PQ
Angular speed of each child is
Explanation of Solution
Both the child in the question are situated in two different locations. But all points on a rigid rotator rotate with the same angular speed
Write the equation to find the angular speed of the child at the outer edge.
Here,
Conclusion:
Substitute
Therefore, angular speed of each child is
(b)
The angular distance travelled by each child in
(b)
Answer to Problem 36PQ
The angular distance moved by each child in
Explanation of Solution
The angular speed of both the children are same. Therefore the
Write the equation to find the
Here,
Rearrange equation (II) to get
Conclusion:
Substitute
Therefore, the angular distance moved by each child in
(c)
The distance in meters moved by the child in
(c)
Answer to Problem 36PQ
The distance moved by child on inner edge of disc is
Explanation of Solution
The distance moved by each child is different since they are placed at different distance from the center of the disc.
Write the equation to find the distance travelled by the child on the outer edge.
Here,
Write the equation to find the distance travelled by the child on the inner edge.
Here,
Conclusion:
Substitute
Substitute
Therefore, the distance moved by child on inner edge of disc is
(d)
The
(d)
Answer to Problem 36PQ
The centripetal force on child on the outer edge is
Explanation of Solution
Write the equation to find the centripetal force on child on outer edge.
Here,
Write the equation to find the centripetal force on child on inner edge.
Here,
Conclusion:
Substitute
Substitute
Therefore, the centripetal force on child on the outer edge is
The centripetal force acting on the child on outer edge is more. As the magnitude of centripetal force increases, the child will experience strong outward force which makes holding on difficult.
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Chapter 12 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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- A square plate with sides of length 4.0 m can rotate about an axle passing through its center of mass and perpendicular to the plate as shown in Figure P14.36. There are four forces acting on the plate at different points. The rotational inertia of the plate is 24 kgm2. Is the plate in equilibrium? FIGURE P14.36arrow_forwardThe uniform thin rod in Figure P8.47 has mass M = 3.50 kg and length L = 1.00 m and is free to rotate on a friction less pin. At the instant the rod is released from rest in the horizontal position, find the magnitude of (a) the rods angular acceleration, (b) the tangential acceleration of the rods center of mass, and (c) the tangential acceleration of the rods free end. Figure P8.47 Problems 47 and 86.arrow_forwardA disk with a radius of 4.5 m has a 100-N force applied to its outer edge at two different angles (Fig. P12.55). The disk has arotational inertia of 165 kg m2. a. What is the magnitude of the torque applied to the disk incase 1? b. What is the magnitude of the torque applied to the disk incase 2? c. Assuming the force on the disk is constant in each case,what is the magnitude of the angular acceleration applied tothe disk in each case? d. Which case is a more effective way of spinning the disk?Describe which quantity you are using to determine effectiveness and why you chose that quantity. FIGURE P12.55arrow_forward
- The angular momentum vector of a precessing gyroscope sweeps out a cone as shown in Figure P11.31. The angular speed of the tip of the angular momentum vector, called its precessional frequency, is given by p=/I, where is the magnitude of the torque on the gyroscope and L is the magnitude of its angular momentum. In the motion called precession of the equinoxes, the Earths axis of rotation processes about the perpendicular to its orbital plane with a period of 2.58 104 yr. Model the Earth as a uniform sphere and calculate the torque on the Earth that is causing this precession. Figure P11.31 A precessing angular momentum vector sweeps out a cone in space.arrow_forwardThe system shown in Figure P13.18 consisting of four particles connected by massless, rigid rods is rotating around the x axis with an angular speed of 2.50 rad/s. The particle masses are m1 = 1.00 kg, m2 = 4.00 kg, m3 = 2.00 kg, and m4 = 3.00 kg. a. What is the rotational inertia of the system around the x axis? b. Using Kr=12I2 (Eq. 13.10), what is the total rotational kinetic energy of the system? c. What is the tangential speed of each of the four particles? d. Considering the system as four particles in motion and using K=i12mvi2, what is the total kinetic energy of the system? How does this value compare with the result obtained in part (b)? FIGURE P13.18arrow_forwardA uniform, hollow, cylindrical spool has inside radius R/2, outside radius R, and mass M (Fig. P10.47). It is mounted so that it rotates on a fixed, horizontal axle. A counterweight of mass m is connected to the end of a string wound around the spool. The counterweight falls from rest at t = 0 to a position y at time t. Show that the torque due to the friction forces between spool and axle is f=R[m(g2yt2)M5y4t2] Figure P10.47arrow_forward
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