a body of mass 2kg is rotating on circular path of radius 0.5m with an angular velocity of 20rad/s if the radius of the path is doubled then new angular velocity will be

Question

Answer

Explanation of Change in Angular Velocity with Change in Radius of Circular Path

Initial conditions: A body of mass 2 kg is rotating on a circular path of radius 0.5 m with an angular velocity of 20 rad/s.

Angular momentum: The angular momentum of the body is given by L = Iω, where I is the moment of inertia and ω is the angular velocity.

Moment of inertia: The moment of inertia of a point mass rotating in a circle is given by I = mr², where m is the mass of the body and r is the radius of the circular path.

Initial angular momentum: Substituting the values, the initial angular momentum of the body is L = (2 kg) x (0.5 m)² x (20 rad/s) = 10 kg m²/s

New radius: If the radius of the circular path is doubled to 1 m, then the new moment of inertia becomes I' = (2 kg) x (1 m)² = 2 kg m².

New angular momentum: Since the angular momentum is conserved, the new angular momentum of the body is L' = L = 10 kg m²/s.

New angular velocity: The new angular velocity of the body is given by ω' = L' / I' = 10 kg m²/s / 2 kg m² = 5 rad/s.

Conclusion

Thus, the new angular velocity of the body is 5 rad/s when the radius of the circular path is doubled to 1 m.

Answer

If angular momentum is conserved, iw =IW
mr^2w= mR^2W
0.5^2(20)=1^2(W)
0.25×20=W
W=5rad/s

Similar Class 12 Doubts

A small Steel of mass M is tied to a string of length R whirled in a horizontal circle with a uniform angular velocity 2w. the string is suddenly pulled so that radius of the circle is half. The new angular velocity will be?

Magnitude of magnetic field due to a circular loop carrying current at its centre is B. If radius and current flowing through the loop are doubled,then new magnetic field at the centre will be A. B/2 B. 2B C. B D. 4B ? The answer is D plz explain.?

Hollow sphere of mass ‘M’ and radius ‘R’ is rotating with angular frequency ‘ω’. It suddenly stops rotating and 75% of kinetic energy is converted to heat. If ‘S’ is the specific heat of the material in J K kg then rise in temperature of the sphere is (M.I. of hollow sphere = MR2?

An electron is rotating around an infinite positive linear charge in a circle of radius of 0.1m,if the linear charge density is 1microcoloumb per metre,then find the velocity of electron in m/s.?

A circular disc is rotating with angular velocity omega. A man standing at edge walks towards the center of disc then how it will affected the angular velocity ?

Top Courses for Class 12

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams