Learning Goal: To use linear and angular momentum to solve simple problems. As shown, a thin metal disk is rolling without slipping along a flat horizontal surface, its velocity in the x direction is v1=41.4 ft/s, and its angular velocity is ω1=23.0 rad/s. The disk is 3.60 ft in diameter, has a thickness of 0.60 in, and has a density of 12 slug/ft3. Positive angular velocity is in the counterclockwise direction.(Figure 1) Part A - Linear momentum Calculate the magnitude of the linear momentum of the disk for the given velocities. Express your answer to three significant figures in slug-foot per second. Part B - Angular momentum about G Calculate the magnitude of the angular momentum about the disk's center of gravity, G, for the given dimensions and angular velocity. Express your answer to three significant figures in slug-foot squared per second.

Learning Goal: To use linear and angular momentum to solve simple problems. As shown, a thin metal disk is rolling without slipping along a flat horizontal surface, its velocity in the x direction is v1=41.4 ft/s, and its angular velocity is ω1=23.0 rad/s. The disk is 3.60 ft in diameter, has a thickness of 0.60 in, and has a density of 12 slug/ft3. Positive angular velocity is in the counterclockwise direction.(Figure 1) Part A - Linear momentum Calculate the magnitude of the linear momentum of the disk for the given velocities. Express your answer to three significant figures in slug-foot per second. Part B - Angular momentum about G Calculate the magnitude of the angular momentum about the disk's center of gravity, G, for the given dimensions and angular velocity. Express your answer to three significant figures in slug-foot squared per second.

Learning Goal:

To use linear and angular momentum to solve simple problems.

As shown, a thin metal disk is rolling without slipping along a flat horizontal surface, its velocity in the x direction is v1=41.4 ft/s, and its angular velocity is ω1=23.0 rad/s. The disk is 3.60 ft in diameter, has a thickness of 0.60 in, and has a density of 12 slug/ft3. Positive angular velocity is in the counterclockwise direction.(Figure 1)

Part A - Linear momentum

Calculate the magnitude of the linear momentum of the disk for the given velocities.

Express your answer to three significant figures in slug-foot per second.

Part B - Angular momentum about G

Calculate the magnitude of the angular momentum about the disk's center of gravity, G, for the given dimensions and angular velocity.

Express your answer to three significant figures in slug-foot squared per second.

Definition Definition Product of the moment of inertia and angular velocity of the rotating body: (L) = Iω Angular momentum is a vector quantity, and it has both magnitude and direction. The magnitude of angular momentum is represented by the length of the vector, and the direction is the same as the direction of angular velocity.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Define Linear momentum and angular momentum:

VIEW

Step 2: Calculate the mass of the disc:

VIEW

Step 3: Calculate the magnitude of the linear momentum of the disc:

VIEW

Step 4: Calculate the magnitude of the angular momentum of the disc:

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 5 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

1. A horizontal platform in the shape of a disk rotates in the horizontal plane about a frictionless vertical axle. The platform has a mass of 150 kg and a radius 2.5m. A student whose mass is 30 kg walks slowly from the rim of the disk towards its center.lf the angular speed is 1.5 rad/s when the boy is at the rim (a)What is the angular speed when the student has reached a point 1.0 m from the center?
a meterstick is balanced at the 60.0 cm mark on a fulcrum. A 63.0 gram object is hung from the 10.0 cm mark and a 150 gram object is hung from the 95.0 cm mark. IF the meterstick is in balance and horizontal, what is the mass of the meterstick? What is the total counter-clockwise torque? WHat is the clockwize torque?
A wrench 0.8 meters long lies along the positive y-axis, and grips a bolt at the origin. A force is applied in the direction of (0,-1,-3) at the end of the wrench. Find the magnitude of the force in newtons needed to supply 100 newton-meters of torque to the bolt. Force: newtons
4
5 1.1
A rotating door is made from four rectangular glass panes, as shown in the figure. The mass of each pane is 94.8 kg. A person pushes on the outer edge of one pane with a force of F = 71.7 N that is directed perpendicular to the pane. Determine the magnitude of the door's angular acceleration. 1.2 m 1.2 m Number i Units
4. 00 10 cm MA = 100 g m² = 100 g mc = 200 g mp = 200 g The four masses are connected by massless rigid sticks. a.) Locate the center of mass. b.) The object rotates about an axis that passes through the center of mass and is parallel to the z-axis. The constant angular velocity is w = 8 rad/s. Calculate the total kinetic energy of this system.
A bowl is rotating on a potter's wheel at constant angular speed as shown. The friction force between his hands and the bowl is 1.70 N total. If the bowl has a diameter of 13.0 cm, how large is the torque on the wheel? Report a positive answer.
6. Find the angular momentum of Earth around the Sun. Also find the angular momentum of a rod about an axis passing through its edge. The length of the rod is 4 m and its mass is 500 g.
12.0 N 30.0% b 10.0 N 9.00 N The figure shows one cylinder inside another. The inner cylinder has a radius of a = 0.5 m and a mass of 2 kg. The outer cylinder has a radius b = 1.5 m and a mass of 12 kg. On the system act 4 forces. Those shown in figure 2 and a friction force. If the magnitude of the frictional torque is 1.75 mN. Determine: a. The net torque vector on the system. (Magnitude and direction) b. The total moment of inertia of the system
2. Let F = 4 i -6 j + 2 k and Let r = 3 i -3 j - 5 k. Find the torque in both Cartesian and polar coordinates. (Find Torque by cross product, find the magnitude of the torque, find the SOLID angle theta and phi since the vector will be in 3 dimensions.) ____________________________________________________________________________________________________________________________________________________________________________ If you could clearly circle the answer I need, that would be great! Thanks!
The angular speed of a rotating platform changes from W equals 2.8 rads/S to W equals 6.8 rad/S at a constant rate as a platform moves through an angle 5.5 rad. The platform has a radius of R equals 28 cm w0=2.8rad/s w=6.8rad/s 0=5.5 radians r=28cm calculate the angular acceleration of the platform a in rad per second squared calculate the tangential acceleration, aT in meters per second squared of a point on the surface of the platform at the outer edge