# Rolling ,Friction and torque

Hi guys.
I had a l'll confusion regarding rolling. Suppose you have a wheel and we set it into motion. If we give it more torque than required to just start rolling it'll accelerate..right? But will it slip greatly if we supply more torque?

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Homework Helper
hi koolraj09! use torque to find the angular acceleration, from that find the linear acceleration if there's no slipping, then use F = ma to find the applied force needed to produce that linear acceleration …

the only (horizontal) applied force is the available friction force, so if that's less than F, the wheel will slip rcgldr
Homework Helper
Torque is opposed by both angular and linear inertia, assuming no slippage, the rate of acceleration is affected by the total inertia, both angular and linear.

If all the mass is at the center than you only have linear factors:

F = m a = T / r
a = T / (m r)
α = a / r = T / (m r2) = T / Il
Il = m r2

If the mass is not at the center, then total inertial equals the sum of angular and linear related components:

I = Ia + Il
c = constant for angular component
Ia = c m r2
I = (c + 1)m r2

For a solid uniform cylinder, c = 1/2
I = Ia + Il = 1/2 m r2 + m r2
Total inertial is triple that of a non-rolling cylinder (zero friction)

α = T / (3/2 m r2) = 2/3 T / (m r2) = 1/3 T / (1/2 m r2)
Angular acceleration is 1/3 of a non-rolling cylinder (zero friction)

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