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A disc of radius R is spun to an angualr...


A disc of radius `R` is spun to an angualr speed `omega_(0)` about its axis and then imparted a horizontal velocity of magnitude `(omega_(0)R)/(4)`. The coefficient of friction is `mu`. The sense of rotation and direction of linear velocity are shown in the figure. The disc will return to its initial position.

A

if the value of `mult0.5`

B

irrespective of the value of `mu`

C

if the value of `0.5ltmult1`

D

if `mugt1`

Text Solution

Verified by Experts


About bottommost point
angular momentum
`L=I_(C)omega_(0)-mv_(0)R` (anticlockwise)
`=(1)/(2)mR^(2)omega-m(omega_(0)(R)/(4))R`

`=(1)/(4)mR^(2)omega_(0)`
`=+` ve or anticlockwise
during slip friction acts about bottommost point. So, its torque is zero or angular momentum about bottommost point should also remain anticlockwise when pure rolling starts. so, figure should be as shown below.
so, the disc will return to its initial position for all value of `mu`.
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A disc of radius R is spun to an angular speed omega_(0) about its axis and then imparted a horizontal velocity of magnitude (omega_(0)R)/(4) (at t=0 ) with its plane remaining vertical. The coefficient of friction between the disc and the plane is mu . The sense of rotation and direction of its linear speed are shown in the figure. The disc returns to its initial point in time T=(25)/(6k mug)omega_(0)R . Find the value of k .

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Knowledge Check

  • A disc of radius R is spum to an angular speed omega about its axis and then imported a horiznotal velociy of magnitude (omega_(0)R)/(4) (at=t=0) with its plane remaining vertical. The coefficent of friction between the disc and the plane is mu The sence of rotation and direction of its lincer speed are shown. in the figure -5.97 choose the correct statement The disc will returen to its intial position :

    A
    if the value of `mult 0.5`
    B
    irrespective of the value of `mu(mugt0)`
    C
    if the value of `0.5ltmult1`
    D
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  • A ring of radius R is rotating with an angular speed omega_0 about a horizontal axis. It is placed on a rough horizontal table. The coefficient of kinetic friction is mu_k . The time after it starts rolling is.

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  • A disc is given an initial angular velocity omega_(0) and placed on a rough horizontal surface as shown Fig. The quantities which will not depend on the coefficient of friction is/are

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    the velocity when rolling begins
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    the work done by the force of friction

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