# Math Help - rotation question

1. ## rotation question

a uniform disc of mass 10 kg radius 1m is placed on a rough horizontal table the coefficient of friction between the disc and the surface is 0.2 a horizontal time varying force is applied on the centre of the disc whose variation with time is as shown in the graph.after 8s the force falls down to zero instantly.find the time at which following occur

a disc rolls without slipping
b disc rolls with slipping
c friction force is less than applied force
d friction force is zero

I KNOW HOW FRICTION WORKS IN CASE OF THIS QUESTION BUT HW TO SOLVE THE PROBLEM PLEASE HELP

2. Originally Posted by prasum
a uniform disc of mass 10 kg radius 1m is placed on a rough horizontal table the coefficient of friction between the disc and the surface is 0.2 a horizontal time varying force is applied on the centre of the disc whose variation with time is as shown in the graph.after 8s the force falls down to zero instantly.find the time at which following occur

a disc rolls without slipping
b disc rolls with slipping
c friction force is less than applied force
d friction force is zero

I KNOW HOW FRICTION WORKS IN CASE OF THIS QUESTION BUT HW TO SOLVE THE PROBLEM PLEASE HELP
from the graph , applied force at the axle as a function of time is $F_a = 10t$

the force of static friction, $f_s$ starts out opposite to $F_a$ and increases until it reaches its maximum, $f_{s\,max}$.

$f_{s\,max} = \mu \cdot F_N = \mu \cdot 10g = 10t
$

$t = \mu g \approx 2 \, sec$

so, reason out the following ...

how does the disk roll in the first two seconds?

how does it roll from t = 2 to t = 8 seconds?

what happens after t = 8 seconds when $F_a$ is removed?

3. can yu tell me what will happen at t=5s t=7s t=7.5s and t=12s

4. Originally Posted by prasum
can yu tell me what will happen at t=5s t=7s t=7.5s and t=12s
Show us what you think is going to happen at those times.

-Dan

5. i think at t=5s and t=12s the body will roll without slipping
at t=7.5s and t=7s the body will roll with slipping
friction force will be less than applied force at t=5s,7s,7.5s
friction force is zero at t=12s