Analyzing Disk, Mass, and Tape System | Physics Problem #14

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This video analyzes the motion of a composite system consisting of a disk, a mass, and a tape, as depicted in the accompanying image. The disk unwinds from the tape, which traverses a frictionless pulley. A mass is suspended from the other end of the tape. The objective is to derive the equations that govern the accelerations of the mass and the disk, as well as the angular acceleration of the disk.
The video employs a systematic approach to address this problem. It commences by establishing the nomenclature and presenting a clear illustration of the system. It then meticulously formulates the constraints that govern the system's motion, expressing the relationship between the displacements of the mass (denoted by m) and the disk (denoted by M and R).
Subsequently, the video leverages Newton's second law of motion to construct the translational equations of motion for both the mass and the disk. To incorporate the rotational aspect of the disk's motion, the rotational equivalent of Newton's second law is introduced, relating the tension in the tape (denoted by T) to the disk's angular acceleration (denoted by α).
By employing a methodical solution technique, the video solves the derived system of equations, ultimately determining the accelerations of the mass (a) and the disk (A), along with the angular acceleration of the disk (α).
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#classicalmechanics #rotationalmechanics #translationalmechanics #engineeringmechanics #dynamics #accelerationanalysis #equationsofmotion #newtonslawsofmotion #physics #engineering #science #physics #mechanics #sigmaphysics

[@ARYAPhysics-HR]

hello bhai did you got tifr mumbai ror not? please aap apna tifr interview experience btaiye.🙏🙏🙏

[@sanjay-cm7dl]

bro 5:11 3/2 should be there no as mr^2/2 for centre but it is in tangent so 3/4 should be there no?

[@SigmaPhysics03]

Good question 😊. Think about it carefully! The body is rolling about the center of mass. Not about the point of contact . If it was rotating about that point of contact (or think about a axis passing through that point of contact) then motion would have been different.

[@SigmaPhysics03]

Actually its all about where you set your origin. i have set my origin in the center of mass of the disc. sorry for the confusion