# Force required to push wheel (not torque)

## Homework Statement

How much force is required to push a wheel of radius 50 mm and moment of inertia 3.21*10^-4 kgm^2 to 20 mph in 5 seconds? The wheel has a mass of 0.29 kg.

The wheel is to be pushed straight and level at its axel 90 degrees to the horizontal.

T = Ia = 5.74 Nm

F = T/r

## The Attempt at a Solution

F = T/r = 5.74/0.05 = 114.8 N

My answer can't be correct because 114.8 N seems far too much force required to accelerate a 50 mm radius wheel to 20 mph in 5 s. That is less force required to push the 200 kg vehicle it supports, and there are another three wheels!

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Never mind, I found my error. I failed to include the negative power value when calculating torque. Torque is 5.7*10^-5, not 5.7! Therefore the force required to push the wheel is just 1.14 * 10^-3 N, which makes much more sense.

Feel free to delete this thread.

Last edited:
rude man
Homework Helper
Gold Member

## Homework Statement

How much force is required to push a wheel of radius 50 mm and moment of inertia 3.21*10^-4 kgm^2 to 20 mph in 5 seconds? The wheel has a mass of 0.29 kg.

The wheel is to be pushed straight and level at its axel 90 degrees to the horizontal.

T = Ia = 5.74 Nm

F = T/r

## The Attempt at a Solution

F = T/r = 5.74/0.05 = 114.8 N

My answer can't be correct because 114.8 N seems far too much force required to accelerate a 50 mm radius wheel to 20 mph in 5 s. That is less force required to push the 200 kg vehicle it supports, and there are another three wheels!
work done by force = acquired linear + rotational kinetic energies.