Question

# 1. You swing a 0.21-kg penguin statue around in a horizontal circle at the end of...

1. You swing a 0.21-kg penguin statue around in a horizontal circle at the end of a 0.84-m long string. The statue’s speed is 6.3 m/s. What is the magnitude of its angular momentum?
 2.A solid uniform cylinder of mass 4.1 kg and radius 0.055 m rolls without slipping at a speed of 0.75 m/s. What is the cylinder’s total kinetic energy?
 3.Calculate the magnitude of the angular momentum of the Earth around the Sun, using the Sun as the origin. The Earth's mass is 5.97×1024 kg and its roughly circular orbit has a radius of 1.50×1011 m. Use a 365-day year with exactly 24 hours in each day.

1) given
m = 0.21 kg
r = 0.84 m
v = 6.3 m/s

angular momentum, L = m*v*r

= 0.21*6.3*0.84

2) given
m = 4.1 kg
R = 0.055 m
v = 0.75 m/s

total kinetic energy = linear kinetic energy + rotational kinetic energy

= (1/2)*m*v^2 + (1/2)*I*w^2

= (1/2)*m*v^2 + (1/2)*(1/2)*m*R^2*w^2

= (1/2)*m*v^2 + (1/4)*m*(R*w)^2

= (1/2)*m*v^2 + (1/4)*m*v^2

= (3/4)*m*v^2 ( v = R*w)

= (3/4)*4.1*0.75^2

3) angular momentum of the earth, L = I*w

= m*r^2*(2*pi/T)

= 5.97*10^24*(1.5*10^11)^2*(2*pi/(365*24*60*60))

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