"a uniform cylinder of mass m and radius r is rolling without slipping. the velocity of its center of mass is v. what is the cylinder's total kinetic energy? "

Explanation:

Given

mass of cylinder is M

radius R

velocity of center of mass is v

As there is no slipping therefore cylinder will rotate as well as translate

Moment of inertia of cylinder

Kinetic Energy of cylinder

Rotational energy

for rolling

where

Total kinetic Energy

where is the circuit diagram ?

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day