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Classical Mechanics
Three objects, a hoop, a disk, and a solid sphere start from the top of a hill and roll without slipping down to the bottom. Which one of the following statements is true?
A. The sphere reaches the bottom first.
B. The disk reaches the bottom first.
C. The object with the greatest mass reaches the bottom first.
D. All three reach the bottom at the same time.
E. The hoop reaches the bottom first.
A. The sphere reaches the bottom first.
B. The disk reaches the bottom first.
C. The object with the greatest mass reaches the bottom first.
D. All three reach the bottom at the same time.
E. The hoop reaches the bottom first.
Classical Mechanics
Which of the following statements is the one that is correct?
A. If all the forces on a body act through the axis of rotation, the angular acceleration will be zero.
B. If two bodies have the same moment of inertia about their centers of mass and the same mass, they must be identical.
C. Two disks roll down an inclined plane without slipping. The one with a smaller radius will always reach the bottom first independent of their masses.
D. Two disks roll down an inclined plane without slipping. The one with a bigger radius will always reach the bottom first independent of their masses.
E. Two disks roll down an inclined plane without slipping. The one with a bigger mass will always reach the bottom first.
A. If all the forces on a body act through the axis of rotation, the angular acceleration will be zero.
B. If two bodies have the same moment of inertia about their centers of mass and the same mass, they must be identical.
C. Two disks roll down an inclined plane without slipping. The one with a smaller radius will always reach the bottom first independent of their masses.
D. Two disks roll down an inclined plane without slipping. The one with a bigger radius will always reach the bottom first independent of their masses.
E. Two disks roll down an inclined plane without slipping. The one with a bigger mass will always reach the bottom first.
Classical Mechanics
Which of the following statements is true?
A. When two hoops with different radii roll down an inclined plane without slipping, they reach the bottom at the same time.
B. If a body is rotating about an axis without any external torques, and its size doubles, it will speed up to double the angular velocity.
C. Two disks roll down an inclined plane without slipping. The one with a smaller radius will always reach the bottom first independent of their masses.
D. When two objects roll down an inclined plane without slipping, they have the same velocity when they reach the bottom only if they have the same mass.
E. The moment of inertia of an object would be different on the surface of the moon than it is on the surface of the Earth
A. When two hoops with different radii roll down an inclined plane without slipping, they reach the bottom at the same time.
B. If a body is rotating about an axis without any external torques, and its size doubles, it will speed up to double the angular velocity.
C. Two disks roll down an inclined plane without slipping. The one with a smaller radius will always reach the bottom first independent of their masses.
D. When two objects roll down an inclined plane without slipping, they have the same velocity when they reach the bottom only if they have the same mass.
E. The moment of inertia of an object would be different on the surface of the moon than it is on the surface of the Earth
Classical Mechanics
A uniform solid cylinder, a hollow cylinder, and a uniform solid sphere are rolling at the same speed on a horizontal table without slipping. If they all have the same mass and radius, which statement is true?
A. They all have the same angular momentum.
B. The hollow cylinder has the most angular momentum.
C. The solid sphere has the most total kinetic energy.
D. The solid cylinder has the greatest rate of rotation.
E. They all have the same kinetic energy of rotation
A. They all have the same angular momentum.
B. The hollow cylinder has the most angular momentum.
C. The solid sphere has the most total kinetic energy.
D. The solid cylinder has the greatest rate of rotation.
E. They all have the same kinetic energy of rotation
Classical Mechanics
A baton consists of a nearly massless rod of length L and two spheres attached to the ends of the rod, whose masses are each M and whose centers are separated by L. The spheres have radius R. If the sphere radius R is not negligible compared to the length L, what is the moment of inertia of the baton about an axis perpendicular to its length and passing through its center?
A. 2MR2
B. 2ML2
C. 2ML2 + 2MR2
D. (1/2) ML2
E. (1/2) ML2 + 2MR2
A. 2MR2
B. 2ML2
C. 2ML2 + 2MR2
D. (1/2) ML2
E. (1/2) ML2 + 2MR2
Classical Mechanics
Which of the following has the largest moment of inertia?
A. A cylinder of mass M with a radius R rotating about its central axis.
B. A hoop of mass M with a radius R rotating about the axis perpendicular to the plane of the hoop and passing through its center.
C. A hoop of mass M with a radius R rotating about a line through its diameter and parallel to the plane of the hoop.
D. A cube of mass M and sides 2R rotating about a line passing through the center of two opposite sides.
E. A rod of mass M and length 2R rotating about a line passing through the center and perpendicular to the rod.
A. A cylinder of mass M with a radius R rotating about its central axis.
B. A hoop of mass M with a radius R rotating about the axis perpendicular to the plane of the hoop and passing through its center.
C. A hoop of mass M with a radius R rotating about a line through its diameter and parallel to the plane of the hoop.
D. A cube of mass M and sides 2R rotating about a line passing through the center of two opposite sides.
E. A rod of mass M and length 2R rotating about a line passing through the center and perpendicular to the rod.
Classical Mechanics
A uniform solid cylinder, a hollow cylinder, and a uniform solid sphere are rolling at the same speed on a horizontal table without slipping. If they all have the same mass and radius, which statement is true?
A. They all have the same angular momentum.
B. The hollow cylinder has the most angular momentum.
C. The solid sphere has the most total kinetic energy.
D. The solid cylinder has the greatest rate of rotation.
E. They all have the same kinetic energy of rotation
A. They all have the same angular momentum.
B. The hollow cylinder has the most angular momentum.
C. The solid sphere has the most total kinetic energy.
D. The solid cylinder has the greatest rate of rotation.
E. They all have the same kinetic energy of rotation
Classical Mechanics
How thick of a concrete wall is required to stop a 6lb round fired at mach six?
Classical Mechanics
5.A block with a mass 0.25 kg sitting on a frictionless surface is connected to a light spring with spring constant 180 N/m .If the block is displaced 15 cm from its equilibrium position and released.The Total Energy and its speed (respectively) of the block when it is 10 cm from equilibrium position is;. Single choice.
(5 Points)
2.0 J and 3.0 m/s
4.05 J and 9 m/s
1.0J and maximum speed
16J and 25 m/s
(5 Points)
2.0 J and 3.0 m/s
4.05 J and 9 m/s
1.0J and maximum speed
16J and 25 m/s
Classical Mechanics
On your wedding day you leave for the church 30.0 minutes before the ceremony is to begin, which should be plenty of time since the church is only 10.0 miles away. On the way, however, you have to make an unanticipated stop for construction work on the road. As a result, your average speed for the first 15 minutes is only 5.0 miles/h. What average speed do you need for the rest of the trip to get you to the church on time?
