A small ring slides on a wire which rotates uniformly at angular frequency ω in a force-free space. If the wire is straight and perpendicular to the axis of rotation, and the ring starts at the axis of rotation, what is the distance of the ring from the axis as a function of time?
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A small ring slides on a wire which rotates uniformly at angular
frequency ω in a...
1. A small bead is free to slide without friction on a rotating wire. The angular...
1. A small bead is free to slide without friction on a rotating wire. The angular speed of the wire is w. In the coordinate system that rotates with the wire, there will be fictitious Coriolis and centrifugal forces, in addition to the real normal force the wire exerts on the bead. Working in this rotating coordinate system, (a) Draw the force diagram, including the fictitious forces. Write down the F=ma equations for the directions parallel and perpendicular to the...
A solid disk rotates in the horizontal plane at an angular velocity of 0.0612 rad/s with...
A solid disk rotates in the horizontal plane at an angular velocity of 0.0612 rad/s with respect to an axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.134 kg·m2. From above, sand is dropped straight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance of 0.398 m from the axis. The sand in the ring has a mass of 0.509 kg. After all...
A solid disk rotates in the horizontal plane at an angular velocity of 0.0647 rad/s with...
A solid disk rotates in the horizontal plane at an angular velocity of 0.0647 rad/s with respect to an axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.199 kg·m2. From above, sand is dropped straight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance of 0.420 m from the axis. The sand in the ring has a mass of 0.499 kg. After all...
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A solid disk rotates in the horizontal plane at an angular velocity of 5.00 × 10-2 rad/s with respect to an axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.15 kg.m2. From above, sand is dropped straight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance of 0.40 m from the axis. The sand in the ring has a mass of 0.50 kg....
2. A bar on a hinge starts from rest and rotates with an angular acceleration α...
2. A bar on a hinge starts from rest and rotates with an angular acceleration α (10 + 61), where α is in rad/s" and 1 is in seconds. Determine the angle in radians through which the bar turns in the first 4.00 s. 4. A dentist's drll starts from rest. After 3.20 s of constant an- gular acceleration, it turns at a rate of 2.51 × 104 rev/min. (a) Find the drill's angular acceleration. (b) Determine the angle (in...
The drawing shows a coil of copper wire that consists of two semicircles joined by straight...
The drawing shows a coil of copper wire that consists of two
semicircles joined by straight sections of wire. In part a the coil
is lying flat on a horizontal surface. The dashed line also lies in
the plane of the horizontal surface. Starting from the orientation
in part a, the smaller semicircle rotates at an angular frequency ω
about the dashed line, until its plane becomes perpendicular to the
horizontal surface, as shown in part b. A uniform magnetic...
Charge is uniformly distributed around a ring of radius R = 8.00 cm, and the resulting...
Charge is uniformly distributed around a ring of radius R = 8.00 cm, and the resulting electric field magnitude E is measured along the ring's central axis (perpendicular to the plane of the ring). At what distance from the ring's center is E maximum?
A conducting bar of length D rotates with angular frequency w about a pivot P at...
A conducting bar of length D rotates with angular frequency w about a pivot P at one end of the bar (see the figure). The other end of the bar is in slipping contact with a stationary conducting wire in the shape of a circle (we only show a small part of that circle to keep the drawing simple). Between point P and the circular wire there is a resistor R as shown. Thus the bar, the resistor and the...
6) A massless turntable is used to play records. Each record is essentially a solid cylinder with...
6) A massless turntable is used to play records. Each record is essentially a solid cylinder with a radius of 0.15 m and mass 0.1 kg. There is a constant frictional force of 0.5 N due to a wire rubbing against the record a distance of 0.05 m from the axis of rotation. Answer the following questions assuming that you apply a tangential force on the record with your finger at a distance of 0.1 m from the axis of...
14. A thin rod (mass lkg and length Im) with its rotation axis perpendicular to its length has a moment of incrtia of 1...
14. A thin rod (mass lkg and length Im) with its rotation axis perpendicular to its length has a moment of incrtia of 1/12 ML2. Two forces are applied to the rod. The points of application and the directions of the forces are indicated in the diagram below. The orientations of the forces remain constant relative to the rod as the rod rotates and produce a constant torque on the rod. through its centre and Rotation axis (a) If the...
1. A small bead is free to slide without friction on a rotating wire. The angular speed of the wire is w. In the coordinate system that rotates with the wire, there will be fictitious Coriolis and centrifugal forces, in addition to the real normal force the wire exerts on the bead. Working in this rotating coordinate system, (a) Draw the force diagram, including the fictitious forces. Write down the F=ma equations for the directions parallel and perpendicular to the...
2. A bar on a hinge starts from rest and rotates with an angular acceleration α (10 + 61), where α is in rad/s" and 1 is in seconds. Determine the angle in radians through which the bar turns in the first 4.00 s. 4. A dentist's drll starts from rest. After 3.20 s of constant an- gular acceleration, it turns at a rate of 2.51 × 104 rev/min. (a) Find the drill's angular acceleration. (b) Determine the angle (in...
The drawing shows a coil of copper wire that consists of two
semicircles joined by straight sections of wire. In part a the coil
is lying flat on a horizontal surface. The dashed line also lies in
the plane of the horizontal surface. Starting from the orientation
in part a, the smaller semicircle rotates at an angular frequency ω
about the dashed line, until its plane becomes perpendicular to the
horizontal surface, as shown in part b. A uniform magnetic...
A conducting bar of length D rotates with angular frequency w about a pivot P at one end of the bar (see the figure). The other end of the bar is in slipping contact with a stationary conducting wire in the shape of a circle (we only show a small part of that circle to keep the drawing simple). Between point P and the circular wire there is a resistor R as shown. Thus the bar, the resistor and the...
6) A massless turntable is used to play records. Each record is essentially a solid cylinder with a radius of 0.15 m and mass 0.1 kg. There is a constant frictional force of 0.5 N due to a wire rubbing against the record a distance of 0.05 m from the axis of rotation. Answer the following questions assuming that you apply a tangential force on the record with your finger at a distance of 0.1 m from the axis of...
14. A thin rod (mass lkg and length Im) with its rotation axis perpendicular to its length has a moment of incrtia of 1/12 ML2. Two forces are applied to the rod. The points of application and the directions of the forces are indicated in the diagram below. The orientations of the forces remain constant relative to the rod as the rod rotates and produce a constant torque on the rod. through its centre and Rotation axis (a) If the...
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