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3 problems tagged with center-of-mass
P0506
Advanced Mechanics › DynamicsBlock Sliding Down a Frictionless Movable Wedge
A wedge ABC of mass $M$ and height $h$ has an inclined surface AC with an angle $\theta$. A small object of mass $m$ is placed at the top A and slides down from rest. All contact surfaces are frictionless. Find:
- The displacement of $M$ when $m$ slides from the top to the bottom.
- The acceleration of $M$ relative to the ground, $a_1$, while $m$ is sliding.
- The acceleration of $m$ relative to $M$, $a'_2$.
- The acceleration of $m$ relative to the ground, $a_2$.
- The interaction force $N$ between $m$ and $M$.
- The normal force $R$ between $M$ and the table.
P0642
Beginner Mechanics › Rotational MotionCenter of Mass of Three Touching Disks
Three uniform disks of the same material and thickness have radii $r_1=a$, $r_2=2a$, and $r_3=2a$. They are welded together in a line such that their edges touch, as shown in the diagram.
- Find the distance of the center of mass of the system from the center of the smallest disk (radius $a$).
- Find the moment of inertia around the center of the disk with radii $r_2=2a$.
P0645
Intermediate Mechanics › Rotational MotionCenter of Mass of a Disk with Hole
A uniform circular disk has a radius $R$. A circular hole with a radius of $R/2$ is cut from it, tangent to the center and the edge of the original disk.
- Find the distance of the center of mass of the remaining part from the center of the original disk.
- Find its moments of inertia about an axis at the center of the original disk and perpendicular to the disk
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