Systems of Particles and Rotational Motion
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Question : 27
Total: 33
Prove the result that the velocity v of translation of a rolling body (like a ring, disc, cylinder or sphere) at the bottom of an inclined plane of a height h is given by
v 2 =
using dynamical consideration (i.e. by consideration of forces and torques).
Note k is the radius of gyration of the body about its symmetry axis, and R is the radius of the body. The body starts from rest at the top of the plane.
using dynamical consideration (i.e. by consideration of forces and torques).
Note k is the radius of gyration of the body about its symmetry axis, and R is the radius of the body. The body starts from rest at the top of the plane.
Solution:
Let M, R, k be the mass, radius and radius of gyration of a body placed at the top A of the inclined plane of height h and angle of inclination θ.
∴ Its total energy at point
Its total energy at point
B = K.E. of translation + K.E. of rotation
According to the principle of conservation of energy we have
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