No Knowledge Points Yet
Knowledge points for this tag are currently being developed.
Browse Problems
3 problems tagged with rotational motion in Kinematics
P0340
Advanced Mechanics › KinematicsAcceleration of Contact Point on Rolling Wheel
As shown in Figure, a wheel with radius $r$ rolls without slipping on the outer surface of a fixed cylinder with radius $R$. The center of the wheel, O, moves with a constant speed $V$.
P0331
Advanced Mechanics › KinematicsKinematics of a Point on a Purely Rolling Ring
A rigid ring with radius $R$ undergoes pure rolling on a rigid horizontal surface. The center of the ring moves forward horizontally with a constant velocity $v_0$. Consider a point P on the ring that is at the same height as the center.
- Find the instantaneous velocity of point P.
- Find the tangential acceleration of point P.
- Find the normal acceleration of point P.
P0718
Expert Mechanics › KinematicsUnwinding Spool
A spool consists of two outer disks of radius $R$ and an inner hub of radius $r$. The total mass is $M$, and the moment of inertia about the center of mass is $I$. A massless string is wrapped around the inner hub in a counter-clockwise fashion. You pull the string with a tension force $T$ at an angle $\theta$ with the horizontal (the string is pulled from the bottom side of the inner hub). The spool rolls without slipping on a rough horizontal floor.
- Depending on the angle $\theta$, the spool can roll to the right (unwinding) or to the left (winding up). What is the geometric condition that determines the direction. Calculate the exact angle $\theta_{crit}$ at which the spool does not roll (i.e., the transition point between forward and backward motion).
- If the string is pulled horizontally ($\theta = 0^\circ$), find the linear acceleration $a$ of the center of mass and the angular acceleration. Assume rolling without slipping.
- If the string is pulled at angle $\theta$ with horizontal, find the linear acceleration $a$ of the center of mass and and the angular acceleration. Assume rolling without slipping.
- You pull the string with constant force $T$ (horizontal, from underside). The center of mass moves a distance $L$. How much work did you do? and what is the displcement and rotational kinetic energy of the system?
- When the string is pulling at constant speed $v$ at an angle $\theta$ with respect to horizontal, the spool is moving forward. Calculate the speed at which the spool is moving.
Practice by Difficulty
Practice all Rotational Motion problems by difficulty level
Problem Sets
No problem sets available for Rotational Motion.