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What is the acceleration of these pure rolling rings?
Question GM3L3: Concepts used in solution F=ma | Constraint equation | Energy conservation | Torque Problem statement Two identical rings of mass M and radius R stand on a rough horizontal surface. The rings are in contact at point P. The radius vector to P makes an angle theta with the horizontal as shown in…
Is it possible to make a pendulum bob undergo uniform circular motion in a vertical plane?
Watch the inner end of string move along the plotted curve. Change parameters and see the effect on the path. Question N1L3: Concepts used in solution Centripetal acceleration | F=ma | Problem statement A small bob of mass m is attached to one end of a light string of length l. How should the other…
How long does it take for a cassette tape to unwind?
Question GM1L2: Concepts used in solution Kinematics Problem statement While listening to a cassette, it took time t for the radius of the unwinding tape reel to be reduced by half. How long will it take for the radius to be reduced by a factor of two again?
Instantaneous axis of rotation and other ways to find velocity of points on a moving triangle.
Question R4L2: Concepts used in solution Instantaneous axis of rotation | Relative velocity | Velocity due to rotation Instantaneous axis of rotation explained in MIT OCW Definition and simulation in 3D available here Problem statement A, B, and C are vertices of a moving rigid equilateral triangle. At a particular instant, A moves with velocity…
What is the force between hemispheres of a charged solid sphere?
Question ES1L3: Concepts used in solution Electric field inside sphere | Spherical coordinates | Center of mass Problem statement What is the net force on the northern hemisphere due to the southern hemisphere of a uniformly charged solid sphere of radius R and the total charge Q?Could this problem be solved using the position of the…
How long does a rotating square plate take to stop?
Question R2L2: Concepts used in solution Moment of inertia | Dimension analysis | Torque | Angular impulse Problem statement A uniform square plate is placed on a rough horizontal floor hinged at one corner. When it is given an angular velocity w about a vertical axis through this corner, as shown in figure(a), it takes…
A fine way to find the moment of inertia of a thin stick without using calculus
Question R1L2: Concepts used in solution Moment of inertia | Dimension analysis | Parallel axis theorem | Scaling Derivation of parallel axis theorem from MIT OCW Problem statement Using just parallel axis theorem and scaling argument, find the moment of inertia of a thin stick about an axis passing through its center and perpendicular to its…
Solving the pulley problem without writing the force equations
Question N1L1: Concepts used in solution Acceleration due to gravity | Center of mass | Vectors Solving the pulley problem by writing the force equations by MIT OCW Problem statement Without writing the force equations, find the acceleration (a) of mass m in the pulley system shown in the figure. Reason the dependence of acceleration…
Finding the gravitational field inside a cavity in a solid sphere
Question G1L2: Concepts used in solution Shell theorem | Superposition principle | Vectors Shell theorem at Hyperphysics and Wikipedia Problem statement A sphere of radius R and uniform density p has within it a spherical cavity of radius r whose center is as shown in the figure. Find the magnitude and direction of the gravitational…
Could a pure rolling disc have zero angular momentum?
Question R3L2: Concepts used in solution L due to translation and rotation | Vector cross product | Right hand rule for L | Derivation of L formula shared by MIT can be found here MIT OCW video on Angular Momentum of Translation and Rotation Problem statement A disc of radius R and mass M rolls without…
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Fun with Physics Problems 