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Chapter 12: Q. 74 (page 334)

A long, thin rod of mass M and length L is standing straight up on a table. Its lower end rotates on a frictionless pivot. A very slight push causes the rod to fall over. As it hits the table, what are

(a) the angular velocity and

(b) the speed of the tip of the rod?

Short Answer

Expert verified

a) Angular velocity is3g/L

b) Velocity is 3gL

Step by step solution

01

Part(a) Step 1: Given information

Mass= M

Length = L

02

Part(a) Step2: Explanation

When Rod is at rest it has only potential energy

PE = Mgh .........................................(1)

Susbtitute h=L/2, as center of mass is at half of the length of the rod.

PE=mgL2..........................(2)

When rod falls on the table then just before touching the surface, potential energy become zero and rod has only kinetic energy .

KE=12I蝇2

Substitute the value of I ,

K.E.=12(ML23)蝇2K.E.=(ML2蝇2)6..................(3)

From law of conservation of energy, PE = KE ,

Equate (2) and (3), we get

(ML2蝇2)6=MgL2鈬�蝇=3gL

03

Part(b) Step1: Given information

Length = L

Mass = M

04

Part(b) Step2: Explanation

Velocity can be calculated by

v = 蝇L

Substitute the value of 蝇 from part(a) we get

v=3gL脳L=3gL

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