Physics chapter 10 part 2
Two masses are located in the x-y plane as follows: a mass of 6kg is located at (0m, 0m), a mass of 4kg is located at (3m, 0m), and a mass of 2kg is located at (0m, 3m). Where is the center of mass of the system?
(1M, 0.5m)
A rigid body is rotating about a fixed axis through the origin. A point on the object located on the x-axis at time t is moving in the positive z direction. What is unit vector in the direction of the angular velocity of the body?
-J
A rigid body is rotating about a fixed axis through the origin. The angular velocity is k, where is positive. What is the unit vector in the direction of the velocity of a point on the body located on the positive y axis?
-i
A rigid body is rotating about a fixed axis through the origin. The angular velocity is K hat, where is positive. What is the unit vector in the direction of the velocity of a point on the body located on the positive y axis?
-i hat
A rigid body is rotating about a fixed axis through the origin. A point on the object located on the x-axis at time t is moving in the positive z direction. What is unit vector in the direction of the angular velocity of the body?
-j
A string is wrapped around a pulley of radius of 2.0cm. The pulley is initially at rest. A constant force of 50N is applied to the string, causing the pulley to rotate and the string to unwind. If the string unwinds 1.2m in 4.9s, what is the moment of inertia of the pulley?
0.20kgm^2
A potter's wheel decelerates from 50rev/min to 30rev/min in 5.0s, with a constant deceleration. What is the magnitude of the deceleration?
0.42rad/s^2
A wheel rotates through an angle of 13.8 rad as it slows down uniformly from 22.0 rad/s to 13.5 rad/s. What is the magnitude of the angular acceleration of the wheel?
10.9 rad/s2
A wrench is acting on a nut. The length of the wrench lies directly to the east of the nut. A force of 150N acts on the wrench at a position 15.0cm from the center of the nut in a direction 30.0 degrees north of east. What is the torque about the center of the nut?
11.3Nm
A pulley has an initial angular speed of 12.5 rad/s and a constant angular acceleration of 3.41 rad/s2. Through what angle does the pulley turn in 5.26 s?
113 rad
A person pushes on a doorknob with a force of 5.00N perpendicular to the surface of the door. The doorknob is located 0.800m from axis of the hinges of the door. The door begins to rotate with an angular acceleration of 2.00 rad/s^2. What is the moment of inertia of the door about the hinges?
2.00kgm^2
A horizontal, 2.00 m long, 5.00 kg uniform beam that lies along the east-west direction is acted on by two forces. At the east end of the beam, a 200 N force pushes downward. At the west end of the beam, a 200 N force pushed upward. What is the torque about the center of mass of the beam?
240 rad/s^2 north
A two dimensional object placed in the xy-plane has three forces acting on it: a force of 3.0N along the x-axis acting at a point (3m,4m)
31 Nm clockwise
In an effort to loosen the bolt on the wheel of a car, a man with a mass of 70 kg steps on the end of a 50-cm tire iron which is extending horizontally from the bolt. How much torque is he applying to the bolt?
340Nm
How long does it take for a rotating object to speed up from 15 to 33.3 rad/s if it had an angular acceleration of 3.45 rad/s^2?
5.30s
A wheel rotated through an angle of 320 degrees as it slows down from 78.0rpm to 22.8rpm. What is the magnitude of the average angular acceleration of the wheel?
5.48 rad/s^2
Consider a rigid body that is rotating. Which of the following is an accurate statement?
All points on the body are moving with the same angular velocity.
Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger centripetal acceleration?
Child A
Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger linear displacement?
Child A
Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger tangential acceleration?
Child A
Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger tangential speed and tangential acceleration?
Child A
Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger tangential speed?
Child A
As you are leaving a building, the door opens outward. If the hinges on the door are on your right, what is the direction of the angular velocity of the door as you open it?
Down. (Right hand rule)
When a rigid body rotates about a fixed axis, all the points in the body have the same centripetal acceleration
False
When a rigid body rotates about a fixed axis, all the points in the body have the same linear displacement
False
When a rigid body rotates about a fixed axis, all the points in the body have the same tangential acceleration
False
When a rigid body rotates about a fixed axis, all the points in the body have the same tangential speed
False
Mass can be considered concentrated at the center of mass for rotational motion.
False, mass of an object can be considered as concentrated at its center if mass only for translational motion.
A dumbbell-shaped object is composed by two equal masses, m, connected by a rod of negligible mass and length r. If I1 is the moment of inertia of this object with respect to an axis passing through the center of the rod and perpendicular to it and I2 is the moment of inertia with respect to an axis passing through one of the masses, it follows that
I2 > I1
When does torque equal zero
In rotational equilibrium, the sun of torques is equal to zero.
What is the quantity used to measure an object's resistance to changes in rotational motion?
Moment of inertia
Two particles of masses m1 and m2 (m1<m2) are located 10 meters apart. Where is the center of mass of the system located?
More than 5 meters but less than 10 meters from the particle of m1
A wheel of radius R is rolling on a horizontal surface. Its center is moving forward with speed v. A point on the wheel a distance r/3 below the center is moving forward at a speed 2v/3. The wheel is
Rolling without slipping
A disk and a hoop of the same mass and radius are released at the same time at the top of an inclined plane and roll without slipping. Which object reaches the bottom of the incline first?
The disk
Jacques and George meet in the middle of a lake while paddling in their canoes. They come to a complete stop and talk for a while. When they are ready to leave, Jacques pushes George's canoe with a force to separate the two canoes. What is correct to say about the final momentum and kinetic energy of the system?
The final momentum is zero kg∙m/s but the final kinetic energy is positive.
Two equal forces are applied to a door at the doorknob.
The first applied perpendicular to the door
Now consider the children's linear acceleration. Which of the following statements are correct?
The last child in the line has the greatest tangential acceleration and the last child in the line has the greatest radial acceleration.
Four children are playing in a field. The children form a line, holding hands. The player at the front of the line starts to spin around faster and faster, causing the others to run around her in a circle. While the line of children is rotating, which of the following statements are correct?
The player at the front of the line has the smallest linear velocity and all the children have the same angular acceleration.
Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger angular displacement?
They have the same non-zero angular displacement.
Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger angular speed?
They have the same non-zero angular speed.
When you are riding a bicycle, in what direction is the angular velocity of the wheel?
To your left
When you ride a bicycle, in what direction is the angular velocity of the wheels?
To your left
An elastic collision of two object is characterized by the following
Total momentum of the system is conserved, total energy of the system remains constant, and total kinetic energy of the system remains constant
Rolling without slipping depends on static friction between the rolling object and the ground.
True
When a rigid body rotates about a fixed axis, all the points in the body have the same angular acceleration
True
When a rigid body rotates about a fixed axis, all the points in the body have the same angular displacement
True
When a rigid body rotates about a fixed axis, all the points in the body have the same angular displacement.
True
When a rigid body rotates about a fixed axis, all the points in the body have the same angular speed
True
When a rigid body rotates about a fixed axis, all the points in the body have the same angular speed
Trye
A child is riding on a merry go round, which is accelerating. What is the relationship between the angular speed and the angular acceleration of the merry go round when the tangential and centripetal accelerations of the child are equal?
a = w^2
A ball is released from rest on a no-slip surface, as shown in the figure. After reaching its lowest point, the ball begins to rise again, this time on a frictionless surface as shown in the figure. When the ball reaches its maximum height on the frictionless surface, it is
at a lesser height as when it was released.
For the system of three particles shown, which have masses M, 2M, and 3M as indicated, where is the center of mass located?
between the particle of mass 2M and the particle of mass 3M
Two cars collide head-on on a level friction-free road. The collision was completely inelastic and both cars quickly came to rest during the collision. What is true about the velocity of this system's center of mass?
it was always zero
A plane, flying horizontally, releases a bomb, which explodes before hitting the ground. Neglecting air resistance, the center of mass of the bomb fragments, just after the explosion
moves along a parabolic path
If a constant net torque is applied to an object, that object will
rotate with constant angular acceleration
A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii. If the three of them are released simultaneously at the top of an inclined plane and do not slip, which one will reach the bottom first?
sphere
The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left), or a distance r/2 from the axis of rotation (right). If you release the hanging blocks simultaneously from rest,
the block at the right lands first.
Two equal forces are applied to a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?
the second at the doorknob
