A non-uniform density cylinder has a radius R=6m. The rotational inertia of this cylinder can be...
A non-uniform density cylinder has a radius R=6m. The rotational inertia of this cylinder can be taken to be I=βMR2, where β is unknown and M is the mass of the cylinder. The cylinder is initially rotating with angular velocity ω0= 1.00rad/s, and is placed on a rough horizontal surface. The speed of the center of mass (CM) of the cylinder, as it is placed on the surface, is 0. The cylinder at first rolls and slips. Just as it begins to roll without slipping, the speed of its center of mass is found to be 3.00 m/s. Calculate β.
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A non-uniform density cylinder has a radius R=6m. The rotational
inertia of this cylinder can be...
A non-uniform cylinder with mass M and radius R rolls without sliding across the floor. If...
A non-uniform cylinder with mass M and radius R rolls without sliding across the floor. If it's mass was 2 kg and its radius 32 cm, and it was rolling at an angular speed of 13 rad/sec, how far up a hill can the cylinder roll without slipping?
A wheel with rotational inertia I=12MR2 about its central axle is set spinning with initial angular...
A wheel with rotational inertia
I=12MR2 about its central axle is set
spinning with initial angular speed ?0 and is then lowered
onto the ground so that it touches the ground with no horizontal
speed. Initially it slips, but then begins to move forward and
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Q7 (15 points): A solid cylinder of mass 5 kg and radius R 0.15 m rolls without slipping on a horizontal surface and is accelerated to the right by a constant force F of magnitude 6 N that is applied at the cylinder by a massless rope as shown in the below figure. Find a) the magnitude of the acceleration of the center of mass of the cylinder, b) the magnitude of the angular acceleration of the cylinder about the...
1977M2. A uniform cylinder of mass M, and radius R is initially at rest on a...
1977M2. A uniform cylinder of mass M, and radius R is initially at rest on a rough horizontal surface. The moment of inertia of a cylinder about its axis is ½MR. A string, which is wrapped around the cylinder, is pulled upwards with a force T whose magnitude is 0.0Mg and whose direction is maintained vertically upward at all times. In consequence, the cylinder both accelerates horizontally and slips. The coefficient of kinetic friction is 0.5 On the diagram below,...
Rolling and slipping: A relative motion approach Mech Name HW-45 6. A cylinder of radius R...
Rolling and slipping: A relative motion approach Mech Name HW-45 6. A cylinder of radius R is placed on top of a wooden board. They are initially at rest. The board is then pulled to the right by a constant horizontal force of magnitude F on a frictionless surface, The cvlinder is observed to roll counterclockwise without slipping cylinder wooden board on the board frictioniess surface At the instant that the board has speed vh, the center-of- mass of the...
Moment of Inertia or Rotational Inertia. A solid cylinder has mass 25kg with radius 60 cm...
Moment of Inertia or Rotational Inertia. A solid cylinder has mass 25kg with radius 60 cm (a) Find its moment of inertia. (b) if the cylinder has a linear speed is 7.7ms, what is the magnitude of the angular momentum of the cylinder? (b) If the cylinder has a linear speed is 7.7m/s, what is the magnitude of the rotational kinetic energy of the cylinder?
A cylinder of mass 11.0 kg and radius 0.260m rolls without slipping on a horizontal surface....
A cylinder of mass 11.0 kg and radius 0.260m rolls without slipping on a horizontal surface. At a particular instant, its center of mass has a speed of 7.30 m/s. Its rotational kinetic energy about its center of mass is then 147J. a) What is in kg m2 its moment of inertia about its center of mass? b) What is in J its linear kinetic energy at that instant? c) What is in J its total kinetic energy at that...
A hollow sphere of radius 0.240 m, with rotational inertia I = 0.0470 kg·m2 about a...
A hollow sphere of radius 0.240 m, with rotational inertia I = 0.0470 kg·m2 about a line through its center of mass, rolls without slipping up a surface inclined at 13.3° to the horizontal. At a certain initial position, the sphere's total kinetic energy is 12.0 J. (a) How much of this initial kinetic energy is rotational? (b) What is the speed of the center of mass of the sphere at the initial position? When the sphere has moved 0.690...
A solid cylinder of radius R and mass m, and moment of inertia mR2/2, starts from rest and rolls down a hill without slipping.
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6. A disk with a mass M, a radius R, and a rotational inertia of I-...
6. A disk with a mass M, a radius R, and a rotational inertia of I- MR is attached to a horizontal spring which has a spring constant of as shown in the diagram. When the spring is stretched by a distance x and then released from rest, the disk rolls without slipping while the spring is attached to the frictionless axle within the center of the disk (a) Calculate the maximum translational velocity of the disk in terms of...
A wheel with rotational inertia
I=12MR2 about its central axle is set
spinning with initial angular speed ?0 and is then lowered
onto the ground so that it touches the ground with no horizontal
speed. Initially it slips, but then begins to move forward and
eventually rolls without slipping.
Q7 (15 points): A solid cylinder of mass 5 kg and radius R 0.15 m rolls without slipping on a horizontal surface and is accelerated to the right by a constant force F of magnitude 6 N that is applied at the cylinder by a massless rope as shown in the below figure. Find a) the magnitude of the acceleration of the center of mass of the cylinder, b) the magnitude of the angular acceleration of the cylinder about the...
1977M2. A uniform cylinder of mass M, and radius R is initially at rest on a rough horizontal surface. The moment of inertia of a cylinder about its axis is ½MR. A string, which is wrapped around the cylinder, is pulled upwards with a force T whose magnitude is 0.0Mg and whose direction is maintained vertically upward at all times. In consequence, the cylinder both accelerates horizontally and slips. The coefficient of kinetic friction is 0.5 On the diagram below,...
Rolling and slipping: A relative motion approach Mech Name HW-45 6. A cylinder of radius R is placed on top of a wooden board. They are initially at rest. The board is then pulled to the right by a constant horizontal force of magnitude F on a frictionless surface, The cvlinder is observed to roll counterclockwise without slipping cylinder wooden board on the board frictioniess surface At the instant that the board has speed vh, the center-of- mass of the...
Moment of Inertia or Rotational Inertia. A solid cylinder has mass 25kg with radius 60 cm (a) Find its moment of inertia. (b) if the cylinder has a linear speed is 7.7ms, what is the magnitude of the angular momentum of the cylinder? (b) If the cylinder has a linear speed is 7.7m/s, what is the magnitude of the rotational kinetic energy of the cylinder?
6. A disk with a mass M, a radius R, and a rotational inertia of I- MR is attached to a horizontal spring which has a spring constant of as shown in the diagram. When the spring is stretched by a distance x and then released from rest, the disk rolls without slipping while the spring is attached to the frictionless axle within the center of the disk (a) Calculate the maximum translational velocity of the disk in terms of...
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