Torque is the cross product of the radius (or arm) and the force applied. A cross product is the product of a scalar, a vector, and the sine of the smallest positive angle between them which returns a vector. You can apply an infinite force at an incident angle whose sine is 0 and generate no torque...thus why you can't fire a cylinder at TDC.
Work is the dot product of force and distance. A dot product is the product of a force, the distance throughout which that force acts and the cosine
of the smallest positive angle between the two which returns a scalar. You can have a force working at an angle with or against the direction that force is acting and still perform work. It just can't be perpindicular (cosine of pi/2 is 0)
oh, also, the correct units for torque are Newton-meters not pound-feet. I look forward to the day when the non-metric units lay down and die.
Didn't read this before i posted sorry.