Does Applying Excess Torque to a Wheel Cause It to Slip?

[koolraj09]

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?
Thanks in Advance.

 

[tiny-tim]

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]

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 / I_l
I_l = m r²

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

I = I_a + I_l
c = constant for angular component
I_a = c m r²
I = (c + 1)m r²

For a solid uniform cylinder, c = 1/2
I = I_a + I_l = 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)