Question

A solid circular disc is spinning with angular velocity and is gently placed upon ough horizontal surface. The angular velocity of rotation when pure rolling starts

Answer 1

Answer:

The acceleration due to friction is given as,

a=

m

f

=

m

μmg

=μg

Angular acceleration due to friction is given as,

α=

I

τ

=

2

1

mR

2

fR

=

R

2μg

The final angular velocity is given as,

ω=ω

0

−αt

ω=ω

0

−

R

2μgt

The final velocity is given as,

v=at

v=μgt

we know that,

v=Rω

μgt=R(ω

0

−

R

2μgt

)

t=

3μg

ω

0

R

Thus, the time is

3μg

ω

0

R

after that the disc will be in