equilibrium,torque and angular momentum lecture 10 tuesday: 17 february 2004
TRANSCRIPT
Equilibrium,Torque and Angular Momentum
Lecture 10
Tuesday: 17 February 2004
Defining Rotational Inertia
•The larger the mass, the smaller the acceleration produced by a given force.
•The rotational inertia I plays the equivalent role in rotational motion as mass m in translational motion.
amF
•I is a measure of how hard it is to get an object rotating. The larger I, the smaller the angular acceleration produced by a given force.
Determining the Rotational Inertia of an Object
1. For common shapes, rotational inertias are listed in tables. A simple version of which is in chapter 11 of your text book.
2. For collections of point masses, we can use :
where r is the distance from the axis (or point) of rotation.
3. For more complicated objects made up of objects from #1 or #2 above, we can use the fact that rotational inertia is a scalar and so just adds as mass would.
I is a function of both the mass and shape of the object. It also depends on the axis of rotation.
Ni
iiirmI
1
2
Torque as a Cross Product
(Like F=Ma)The direction of the Torque is always in the direction of
the angular acceleration.
• For objects in equilibrium, =0 AND F=0
sinFr
Fr
Torque Corresponds to Force
Torque Corresponds to Force
• Just as Force produces translational acceleration (causes linear motion in an object starting at rest, for example)
• Torque produces rotational acceleration (cause a rotational motion in an object starting from rest, for example)
• The “cross” or “vector” product is another way to multiply vectors. Cross product results in a vector (e.g. Torque). Dot product (goes with cos ) results in a scalar (e.g. Work)
• r is the vector that starts at the point (or axis) of rotation and ends on the point at which the force is applied.
Does an object have to be moving in a circle to have angular momentum?
• No.
• Once we define a point (or axis) of rotation (that is, a center), any object with a linear momentum that does not move directly through that point has an angular momentum defined relative to the chosen center as
p
prL
