A cylinder with rotational inertia I1 = 3.2 kg · m2 rotates clockwise about a vertical...
A cylinder with rotational inertia
I1 = 3.2 kg · m2
rotates clockwise about a vertical axis through its center with angular speed
ω1 = 5.8 rad/s.
A second cylinder with rotational inertia
I2 = 1.2 kg · m2
rotates counterclockwise about the same axis with angular speed
ω2 = 6.2 rad/s.
If the cylinders couple so they have the same rotational axis, what is the angular speed of the combination (in rad/s)?
What percentage of the original kinetic energy is lost to friction?
Homework Answers
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A cylinder with rotational inertia
I1 = 3.2 kg · m2
rotates clockwise about a vertical...
A cylinder with moment of inertia I1 rotates with angular velocity ω0 about a frictionless vertical axle.
A cylinder with moment of inertia I1 rotates with angular velocity ω0 about a frictionless vertical axle. A second cylinder, with moment of inertia I2, initially not rotating, drops onto the first cylinder (Fig. P8.55). Because the surfaces are
rough, the two eventually reach the same angular velocity,ω.Figure P8.55(a) Calculate ω. (Use I1
for I1, I2 for I2, and w0
for ω0 in yourequation.)(b) Show that energy is lost in this situation (Do this on
paper.Your instructor may ask you to turn in this work.), and...
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In the diagram, Disk 1 has a moment of inertia of 4.20 kg · m2 and...
In the diagram, Disk 1 has a moment of inertia of 4.20 kg · m2 and is rotating in the counterclockwise direction with an angular speed of 6.90 rad/s about a frictionless rod passing through its center. A second disk rotating clockwise with an angular speed of 8.50 rad/s falls from above onto Disk 1. The two then rotate as one in the clockwise direction with an angular speed of 2.80 rad/s. Determine the moment of inertia of Disk 2.
Part B. The answer is 1.07 rad/s. (12.2.20) In the diagram below, the upper cylinder has...
Part B.
The answer is 1.07 rad/s.
(12.2.20) In the diagram below, the upper cylinder has mass M1 = 3.00 kg and the lower cylinder has mass M2 = 2.00 kg. Their radii are a and 3a, where a = 10.0 cm, as shown. Initially M1 is rotating clockwise at 8.00 rad/s and M2 is rotating counterclockwise at 4.00 rad/s. They are both rotating about the same axis passing through the centers of the two cylinders. (a) M1 is dropped...
If an object has a moment of inertia 21 kg-m2 and rotates with an angular speed...
If an object has a moment of inertia 21 kg-m2 and rotates with an angular speed of 113 radians/s, what is its rotational kinetic energy? i la- ro
A sanding disk with rotational inertia 5.8 x 10 kg m2 is attached to an electric...
A sanding disk with rotational inertia 5.8 x 10 kg m2 is attached to an electric drill whose motor delivers a torque of magnitude 20 N-m about the central axis of the disk. About that axis and with torque applied for 42 ms, what is the magnitude of the (a) angular momentum and (b) angular velocity of the disk? (a) Number Unii (b) Number Units
A disk with a rotational inertia of 5.0 kg · m2 and a radius of 0.25...
A disk with a rotational inertia of 5.0 kg · m2 and a radius of 0.25 m rotates on a frictionless fixed axis perpendicular to the disk and through its center. A force of 8.0 N is applied along the rotation axis. The angular acceleration of the disk is? The answer is 0, but how?
A horizontal platform in the shape of a circular disk rotates on a frictionless bearing about...
A horizontal platform in the shape of a circular disk rotates on a frictionless bearing about a vertical axle through the center of the disk. The platform has a radius of 3.40 m and a rotational inertia of 464 kg·m2 about the axis of rotation. A 68.9 kg student walks slowly from the rim of the platform toward the center. If the angular speed of the system is 1.48 rad/s when the student starts at the rim, what is the...
A disk with moment of inertia 9.15 × 10−3 kg∙m^2 initially rotates about its center at...
A disk with moment of inertia 9.15 × 10−3 kg∙m^2 initially rotates about its center at angular velocity 5.32 rad/s. A non-rotating ring with moment of inertia 4.86 × 10−3 kg∙m^2 right above the disk’s center is suddenly dropped onto the disk. Finally, the two objects rotate at the same angular velocity ?? about the same axis. There is no external torque acting on the system during the collision. Please compute the system’s quantities below. 1. Initial angular momentum ??...
A horizontal platform in the shape of a circular disk rotates on a frictionless bearing about...
A horizontal platform in the shape of a circular disk rotates on
a frictionless bearing about a vertical axle through the center of
the disk. The platform has a radius of 4.64 m and a rotational
inertia of 141 kg·m2 about the axis of rotation. A 53.2
kg student walks slowly from the rim of the platform toward the
center. If the angular speed of the system is 1.48 rad/s when the
student starts at the rim, what is the...
A cylinder with moment of inertia I1 rotates with angular velocity ω0 about a frictionless vertical axle. A second cylinder, with moment of inertia I2, initially not rotating, drops onto the first cylinder (Fig. P8.55). Because the surfaces are
rough, the two eventually reach the same angular velocity,ω.Figure P8.55(a) Calculate ω. (Use I1
for I1, I2 for I2, and w0
for ω0 in yourequation.)(b) Show that energy is lost in this situation (Do this on
paper.Your instructor may ask you to turn in this work.), and...
Part B.
The answer is 1.07 rad/s.
(12.2.20) In the diagram below, the upper cylinder has mass M1 = 3.00 kg and the lower cylinder has mass M2 = 2.00 kg. Their radii are a and 3a, where a = 10.0 cm, as shown. Initially M1 is rotating clockwise at 8.00 rad/s and M2 is rotating counterclockwise at 4.00 rad/s. They are both rotating about the same axis passing through the centers of the two cylinders. (a) M1 is dropped...
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A sanding disk with rotational inertia 5.8 x 10 kg m2 is attached to an electric drill whose motor delivers a torque of magnitude 20 N-m about the central axis of the disk. About that axis and with torque applied for 42 ms, what is the magnitude of the (a) angular momentum and (b) angular velocity of the disk? (a) Number Unii (b) Number Units
A horizontal platform in the shape of a circular disk rotates on
a frictionless bearing about a vertical axle through the center of
the disk. The platform has a radius of 4.64 m and a rotational
inertia of 141 kg·m2 about the axis of rotation. A 53.2
kg student walks slowly from the rim of the platform toward the
center. If the angular speed of the system is 1.48 rad/s when the
student starts at the rim, what is the...
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