**Practice Exam Rotation II**- A solid sphere with radius \( R \) and a cylindrical hoop with radius \( \frac{1}{3} R \) race down an incline of height \( H \). Determine the final speed of each object as it reaches the bottom of the incline (assume the masses are the same).**Diagrams and Equations:**1. **Cylinder at axis, disc center:** - Diagram shows a cylinder rolling down an incline. - Moment of Inertia: \( \frac{1}{2} MR^2 \)2. **Cylindrical hoop, shear center:** - Diagram shows a hoop rolling down an incline. - Moment of Inertia: \( MR^2 \)3. **Solid sphere, about diameter:** - Diagram shows a sphere rolling down an incline. - Moment of Inertia: \( \frac{2}{5} MR^2 \)4. **Inclined disk or cylinder:** - Diagram shows an inclined disk or cylinder. - Moment of Inertia: \( \frac{1}{2} MR^2 \)The diagrams provide visual representations of each object on an incline with their respective moments of inertia equations, which are key for determining their final speeds at the bottom of the incline.

Given data, Assuming the height of the inclined plane is 'H'. Mass is m v is the velocity.

Kota A solid sphere radius R and a cylindrical hoop radius 1/3 R race down an incline of height H. Determine the final speed of each object as it reaches the bottom of the incline (assume the masses are the same).

Kota A solid sphere radius R and a cylindrical hoop radius 1/3 R race down an incline of height H. Determine the final speed of each object as it reaches the bottom of the incline (assume the masses are the same).

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter12: Rotation I: Kinematics And Dynamics

Section: Chapter Questions

Problem 62PQ: Problems 62 and 63 are paired. 62. C A disk is rotating around a fixed axis that passes through its...

See similar textbooks

Similar questions

Problems 62 and 63 are paired. 62. C A disk is rotating around a fixed axis that passes through its center and is perpendicular to the face of the disk. Consider a point on the rim of the disk (point R) and another point halfway between the center and the rim (point H) at one particular instant. a. How does the angular speed v of the disk at point H compare with the angular speed of the disk at point R? b. How does the tangential speed of the disk at point H compare with the tangential speed of the disk at point R? c. Suppose we pick a point H on the disk at random (by throwing a dart, for example), and we compare the speeds at that point with the speeds at point R. How will the answers to parts (a) and (b) be different? Explain.
Ethan and Joseph are riding on a merry-go-round. Ethan rides on a horse at the outer rim of the circular platform, twice as far from the center of the circular platform as Joseph, who rides on an inner horse. (i) When the merry-go-round is rotating at a constant angular speed, what is Ethans angular speed? (a) twice Josephs (b) the same as Josephs (c) half of Josephs (d) impossible to determine (ii) When the merry-go-round is rotating at a constant angular speed, describe Ethans tangential speed from the same list of choices.
Model the Earth as a uniform sphere. (a) Calculate the angular momentum of the Earth due to its spinning motion about its axis. (b) Calculate the angular momentum of the Earth due to its orbital motion about the Sun. (c) Explain why the answer in part (b) is larger than that in part (a) even though it takes significantly longer for the Earth to go once around the Sun than to rotate once about its axis.
Gravity is an example of a central force that acts along the line connecting two spherical masses. As a planet orbits its sun, (a) how much torque does the suns gravitational force exert on the planet? (b) What is the change in the planets orbital angular momentum?
(a) What is the angular momentum of the Moon in its orbit around Earth? (b) How does this angular momentum compare with the angular momentum of the Moon on its axis? Remember that the Moon keeps one side toward Earth at all times. (c) Discuss whether the values found in parts (a) and (b) seem consistent with the fact that tidal effects with Earth have caused the Moon to rotate with one side always facing Earth.
Review. A piece of putty is initially located at point A on the rim of a grinding wheel rotating at constant angular speed about a horizontal axis. The putty is dislodged from point A when the diameter through A is horizontal. It then rises vertically and returns to A at the instant the wheel completes one revolution. From this information, we wish to find the speed v of the putty when it leaves the wheel and the force holding it to the wheel. (a) What analysis model is appropriate for the motion of the putty as it rises and falls? (b) Use this model to find a symbolic expression for the time interval between when the putty leaves point A and when it arrives back at A, in terms of v and g. (c) What is the appropriate analysis model to describe point A on the wheel? (d) Find the period of the motion of point A in terms of the tangential speed v and the radius R of the wheel. (e) Set the time interval from part (b) equal to the period from part (d) and solve for the speed v of the putty as it leaves the wheel. (f) If the mass of the putty is m, what is the magnitude of the force that held it to the wheel before it was released?
The angular position of a rod varies as 20.0t2radians from time t=0 . The rod has two beads on it as shown in the following figure, one at 10 cm from the ratation axis and the other at 20 cm from the rotation axis. (a) What is the instantaneous angular velocity of the rod at t=5s ? (b) What is the angular acceleration of the rod? (c) What are the tangential speeds of the beads at t=5s ? (d) What are the tangential acceleration of the beads at t=5s ? (e) What are the centripetal accelerations of the beads at t=5s ?
A record is spinning at the rate of 25 rpm. If a ladybug is sitting 10 cm from the center of the record: a. What is the angular velocity of the ladybug? (in rev/sec) b. What is the tangential speed of the ladybug? (in cm/sec)
Which will experience tangential acceleration? Explain. a. all particles b. particles with 0 angular accceleration c. particles with changing angular acceleration d. particles with constant angular acceleration
***IMAGE IS ATTACHED** ANGULAR ACCELARATION = 2 rad/s^2 A spinning disk is rotating at a rate of 2 rad/s in the counterclockwise direction as shown in the figure. Find the wheel's angular velocity after 4 s. Find the angle through which the wheel has turned after 4 s in radians. Find the magnitude of the velocity (speed) of a point located at r = 20 cm from the center of the wheel after 4 s. Find the magnitude of the parallel acceleration of the point in the above part.
Two people start at the same place and walk around a circular lake in opposite directions. One has an angular speed of 1.79 x 103 rad/s, while the other has an angular speed of 4.23 x 103 rad/s. How long will it be before they meet? End Start Number i Units
Two children, Sara and Elena, ride on a merry-go-round. Sara is at a greater distance from the axis of rotation than Elena. Which of the following is a true statement? a. Sara has a greater tangential speed than Elena. b. Sara and Elena have the same tangential speed. c. Sara has a smaller angular speed than Elena. d. Sara has a smaller tangential speed than Elena.