A solid disk of 50 kg and radius 0.4m , initially at rest . Rolls down a hill th

Question

A solid disk of 50 kg and radius 0.4m , initially at rest . Rolls down a hill that is vertical height of 20m above the ground. A)the final linear speed B) the final angular speed of he disk when it reaches the ground A solid disk of 50 kg and radius 0.4m , initially at rest . Rolls down a hill that is vertical height of 20m above the ground. A)the final linear speed B) the final angular speed of he disk when it reaches the ground A)the final linear speed B) the final angular speed of he disk when it reaches the ground

Explanation / Answer

A)

Here ,

let the final linear speed is v

Now , for rolling ,

v = r*w

Now , using conservation of energy

0.5 * I*w^2 + 0.5 mv^2 = mgh

0.5 * 0.5 * m *r^2* v^2/r^2 + 0.5 * m * v^2 = m * g * h

0.75 * v^2 = 9.8 * 20

v = 16.2 m/s

the linear speed of disk is 16.2 m/s

b)

Now, for angular speed , w ,

w = V/r

w = 16.2/0.4

w = 40.4 rad/s

the final angular speed is 40.4 rad/s

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