A disc of mass `m` and radius `R` moves in the `x-y` plane as shown in Fig. The angular momentum of the disc about the origin `O` at the instant shown is

Options

A. `-5/2mR^(2)omegahatk`
B. `7/3mR^(2)omegahatk`
C. `-9/2mR^(2)omegahatk`
D. `5/2mR^(2)omegahatk`

Answer

A

Explanation

`vecL_(O)=I_(CM)vecomega+m(vecrxxvecv)=1/2mR^(2)omegahatk+m(4Rhati+3Rhatk)xx(omegaRhati)`
`=1/2mR^(2)omegahatk-3mRomegahatk=-5/2mR^(2)omegahatk`