CBSE (Science) Class 11CBSE
Share

A Solid Cylinder of Mass 20 Kg Rotates About Its Axis with Angular Speed 100 Rad S–1. the Radius of the Cylinder is 0.25 M. What is the Kinetic Energy Associated with the Rotation of the Cylinder? What is the Magnitude of Angular Momentum of the Cylinder About Its Axis? - CBSE (Science) Class 11 - Physics

ConceptTorque and Angular Momentum

Question

A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s–1. The radius of the cylinder is 0.25 m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of the angular momentum of the cylinder about its axis?

Solution 1

Mass of the cylinder, m = 20 kg

Angular speed, ω = 100 rad s–1

Radius of the cylinder, r = 0.25 m

The moment of inertia of the solid cylinder:

I = (mr^2)/2

= 1/2 xx 20 xx (0.25)^2

= 0.625 "kg m"^2

:.Kinetic energy = 1/2Iomega^2

= 1/2 xx 6.25 xx (100)^2 = 3125J

∴Angular momentum, L = Iω

= 6.25 × 100

= 62.5 Js

Solution 2

M = 20 kg

Angular speed, w = 100 rad s-1; R = 0.25 m

Moment of inertia of the cylinder about its axis =1/2 MR2 = 1/2 x 20 (0.25)2 kg m2 = 0.625 kg m2

Rotational kinetic energy,

Er = 1/2 Iw2 = 1/2 x 0.625 x (100)2 J = 3125 J

Angular momentum, L = Iw = 0.625 x 100 Js= 62.5 Js

Is there an error in this question or solution?

APPEARS IN

NCERT Solution for Physics Textbook for Class 11 (2018 to Current)
Chapter 7: System of Particles and Rotational Motion
Q: 12 | Page no. 179

Video TutorialsVIEW ALL 

Solution A Solid Cylinder of Mass 20 Kg Rotates About Its Axis with Angular Speed 100 Rad S–1. the Radius of the Cylinder is 0.25 M. What is the Kinetic Energy Associated with the Rotation of the Cylinder? What is the Magnitude of Angular Momentum of the Cylinder About Its Axis? Concept: Torque and Angular Momentum.
S