Physics Chapter 9
Two points are located on a rigid wheel that is rotating with decreasing angular velocity about a fixed axis. Point A is located on the rim of the wheel and point B is halfway between the rim and the axis. Which one of the following statements concerning this situation is true?
Both points have the same instantaneous angular velocity
A 2.0 kg solid disk rolls without slipping on a horizontal surface so that its center proceeds to the right with speed 5m/s. The point A is the uppermost point on the disk and the point B is along the horizontal line that connects the center of the disk to the rim. What is the direction of the disk's angular velocity?
Into the paper (away from you)
A 2.0 kg hoop rolls without slipping on a horizontal surface so that its center proceeds to the right with a constant linear speed of 6.0 m/s. Which one of the following statements is true concerning the angular momentum of this hoop?
It points into the paper
A child standing on the edge of a freely spinning merry-go-round moves quickly to the center. Which one of the following statements is necessarily true concerning this event and why?
The angular speed of the system increases because the moment of inertia of the system has decreased.
Three objects are positioned along the x axis as follows: 4.4kg at x= +1.1 m, 3.7kg at x+-0.80m, and 2.9kg at x=-1.6m. The acceleration due to gravity is the same everywhere. What is the distance from the location of the center of gravity to the location of the center of mass for this system?
0 meters
Planets A and B are uniform solid spheres that rotate at a constant speed about axes through their centers. Although B has twice the mass and three times the radius of A, each planet has the same rotational kinetic energy. What is the ratio wB/wA of their angular speeds?
0.093 RKE = (1/2)*I*w^2 w = v/r KE(1) = (1/2)*(2/5)*M*R^2*(v^2/R^2) KE(2) = (1/2)*(2/5)*2M*3R^2*(v^2/(3R^2)) KE 1 = KE2 w(1) = SQRT w(2)
Two equal spheres, labeled A and B in the figure, are attached to a massless rod with a frictionless pivot at the point P. The system is made to rotate clockwise with angular speed w on a horizontal, frictionless tabletop. Sphere A collides with and sticks to another equal sphere that is at rest on the tabletop. Note: the mass of all three spheres are equal. What is the angular speed of the system immediately after the collision?
0.56w I(initial)= MR^2 + (1/2)MR^2 = (5/4)MR^2 I(final) = (2M)R^2 + (1/2)MR^2 = (9/4)MR^2 L(initial) = L(final) I(initial)w = I(final)w(final)
A horizontal 10-m plank weighs 100 N. It rest on two supports that are placed 1.0m from each end as shown in the figure. How close to one end can an 800N person stand without causing the plank to tip?
0.5m m*g*(1/2)r
A uniform disk of radius 1.2 m and mass .60kg is rotating at 25 rad/s around an axis that passes through its center and is perpendicular to the disk. A rod makes contract with the rotating disk with a force of 4.5 N at a point of .75m from the axis of rotation as shown. The disk is brought to a stop in 5s. What is the coefficient of kinetic friction for the two materials in contact?
0.64 w(initial) = w(final) = w(initial) + angular acceleration*time I = mr^2/2 Torque = I* angular acceleration Force at x = Torque/x Coefficient = Force(above)/Force(given)
A certain satellite in a circular orbit of radius (r) remains vertically above a certain point on Earth's equator. Which of the following expressions correctly gives r in terms of w (the angular velocity of Earth's rotation about its axis). M (the mass of the Earth), and G (the universal gravitational constant)?
r^3 = GM/w^2
Consider the following three objects, each of the same mass and radius: 1) Solid Sphere 2) Solid Disk 3) Hoop All three are release from rest at top of an inclined plane. The three objects proceed down the incline undergoing rolling motion without slipping. In which order do the objects reach the bottom of the incline?
1,2,3
Joe is painting the floor of his basement using a paint roller. The roller has a mass of 2.4 kg and a radius of 3.8 cm. In rolling the roller across the floor, Joe applies a force F=16N directed at an angle of 35 as shown. Ignoring the mass of the roller handle, what is the magnitude of the angular acceleration of the roller?
1.0 * 10^2 rad/s^2 [(F/m)/r]*sin(theta)
Two skaters, each of mass 40 kg, approach each other along parallel paths that are separated by a distance of 2m. Both skaters have a speed of 10 m/s. The first skater carries a 2m pole that may be considered massless. As he passes the pole, the second skater catches hold of the end. The two skaters then go around in a circle about the center of the pole. What is the angular speed of the skaters after they have linked together?
10 rad/s
A ceiling fan has five blades, each with a mass of .34 kg and a length of .66m. The fan is operating in its "low" setting at which the angular speed is 9.4 rad/s. If the blades can be approximated as uniform thin rods that rotate about one end, what is the total rotational kinetic energy of the five blades?
11 J RKE = (1/2)*Iw^2 I (one blade) = 1/3MR^2 I (all blades) =
A horizontal uniform plank is supported by ropes I and II at points P and Q, respectively, as shown above. The two ropes have negligible mass. The tension in rope I is 187.5 N. The point at which rope II is attached to the plank is now moved to point R halfway between point Q and point C, the center of the plank. The plank remains horizontal. Which of the following are most nearly the new tensions in the two ropes?
125N and 250N Torque 1 = Torque 2 Torque = F*R __F1 *2R = __F2*R F2 must be 2 time F1 F1+F2 =
A hollow sphere of radius .25m is rotating at 13 rad/s about an axis that passes through its center. The mass of the sphere 3.8kg. Assuming a constant net torque is applied to the sphere, how much work is required to bring the sphere to a stop? (I (hollow sphere) - (2/3)mr^2)
13 J W = ΔK = (1/2)Iω^2 = (1/3)MR^2
Consider four point masses located as shown in the sketch. The acceleration due to gravity is the same everywhere. What is the x coordinate of the center of gravity for this system?
3m (m1*x1)+(m2*x2)+(m3*x3)+(m4*x4) / (x1+x2+x3+x4)
A ball attached to a string starts at rest and undergoes a constant angular acceleration as it travels in a horizontal circle of radius .30m. After .65 seconds, the angular speed of the ball is 9.7 rad/s. What is the tangential acceleration of the ball?
4.5 m/s^2 w(final) = w(initial) + angular accel.*t a = r*angular acceleration
A solid sphere of radius R rotates about a diameter with an angular speed w. The sphere then collapses under the action of internal forces to a final radius R/2. What is the final angular speed of the sphere?
4w
The rotational inertia of a sphere mass M and radius R about a diameter is (2/5)MR^2. The rotational inertia about an axis tangent to the sphere is?
7/5 MR^2 I+MR^2
A 2.0 kg hoop rolls without slipping on a horizontal surface so that its center proceeds to the right with a constant linear speed of 6.0 m/s. What is the total kinetic energy of the hoop?
72 J mv^2
The drawling shows the top view of a door that is 1.68 m wide. Two forces are applied to the door as indicated. What is the magnitude of the net torque on the door with respect to the hinge?
8.3 N*m
Three objects are attached to a massless rigid rod that has an axis of rotation as shown. Assuming all of the mass of each object is located at the point shown for each, calculate the moment of inertia of this system.
9.1 kg*m^2 I = Sum mr^2
A solid sphere rolls without slipping along a horizontal surface. What percentage of its total kinetic energy is rotational kinetic energy?
29%
A solid cylinder of radius 0.35m is released from rest from a height of 1.8m and rolls down the incline as shown. What is the angular speed of the cylinder when it reaches the horizontal surface?
14 rad/s mgh = ½m(ωr)² + ¼mr²ω²
A string is wrapped around a pulley of radius 0.20m and moment of inertia .40k*m^2. The string is pulled with a force of 28N. What is the magnitude of the resulting angular acceleration of the pulley?
14 rad/s^2 T(torque) = F*R = I*angular acceleration
A particle of mass 2kg is moving in the xy-plane at a constant speed of 1.8m/s in the + x-direction along the line y=4m. As the particle travels from x=-3m to x=+3m, the magnitude of its angular momentum with respect to the origin is...?
14.4 kg*m^2/s L= r * p r is the y= value p=m*v
A massless frame in the shape of a square with 2m sides has a 1kg ball at each corner. What is the moment of inertia of the four balls about an axis through the corner marked O and perpendicular to the plane of paper?
16 kg*m^2
A certain merry-go-round is accelerated uniformly from rest and attains an angular speed of 1.2 rad/s in the first 18 seconds. If the next applied torque is 1200 N*m, what is the moment of inertia of the merry-go-round?
18000 kg*m^2 w = w(initial) + angular acceleration * time Torque = I*angular acceleration
A wheel, originally rotating at 126 rad/s undergoes a constant deceleration of 5 rad/s^2. What is its angular speed after it has turned through an angle of 628 radius?
19 rad/s
A 2.0 kg solid cylinder of radius 0.5m rotates at a rate of 40rad/s about its cylindrical axis. What power is required to bring the cylinder to rest in 10s?
20 W
A steady horizontal force F of magnitude 21 N is applied at the axle of a solid disk as shown. The disk has mass 2.0kg and diameter 0.10m. What is the linear speed of the center of the disk after it has moved 12m?
22 m/s or 13 m/s Torque = Force*Radius Torque = Inertia*angular acceleration Angular acceleration*Radius = a V^2 = U^2 + 2ax U^2 = 0
One end of a rope is tied to the handle of a horizonally-oriented and uniform door. A force F is applied to the other end of the rope as shown in the drawing. The door has a weight of 145N and is hinged on the right. What is the maximum magnitude of F for which the door will remain at rest?
265 N Torque = (Weight*Length of Door) / 2 Torque = F*Rope*sin(theta)
