Some examples of torque as a vector
Let's do a few simple examples.
- Barb the Plumber is hard at work removing a clogged pipe.
As she places her wrench around the head of the bolt,
the 30-cm handle sticks vertically upwards.
Barb then pulls on the end of the handle
with a force of 250 N to the South.
What is the torque exerted by Barb around the head of the bolt?
- The engine of a spacecraft sticks out from the center
of the ship on a long spar. Its position relative
to the center of the ship is
r = ( 32 m) i + ( 22 m) j - ( 13 m) k
A passing asteroid exerts a gravitational force on the
F = ( 0.2 N) i - ( 0.1 N) j + ( 1.2 N) k
What is the torque on the engine around the center
of the spaceship?
A ball of mass M = 3 kg
is attached to a massless rod of length L = 6 m.
The rod is attached to a pivot and is initially horizontal.
Fred holds everything in place.
- What is the moment of inertia of the arm-plus-ball
around the pivot?
Fred now releases the ball and rod, which start to swing
A moment later, the rod has swung by an angle
β from the horizontal.
- What is the torque on the ball due to gravity at this moment?
- If the ball swings just a teeny little extra angle dβ,
how much work will the torque do during that teeny motion?
- Write down -- but don't evaluate --
an integral which expresses the amount of work done
by the torque as the rod swings
from its starting point to the current angle β.
- Write down -- and DO evaluate --
an integral showing the work done by the torque
as the rod rotates from its starting point to
its lowest point.
- What is the angular velocity of the rod when it reaches
its lowest point?
- What is the linear velocity of the ball when it reaches
its lowest point?
- Is there any easier way to do this particular problem?