- #1
zkhandwala
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Hi - I'm undertaking a self-study of calculus-based physics 101 using Sears/Zemansky's 'University Physics' text (12th ed). So far so good, but I've hit a mental stumbling block on the topic of angular momentum and am hoping this forum can help me get past it...
The text begins by referring to an arbitrary 3-D rigid body rotating around the z-axis. This same body was used to discuss rotational energy, inertial moment calculation, etc. The text then considers one arbitrary particle of the body, and defines the angular momentum of the particle as [tex]\vec{r}[/tex] x m[tex]\vec{v}[/tex]. What's immediately odd to me about this is that [tex]\vec{r}[/tex] is considered relative to the origin of the coordinate system, when in previous sections it had been given as relative to the axis of rotation. Annoyed , I accept this and move on, but...
...Then the notion is introduced that the rate of change of this particle's angular momentum is equal to the torque applied to the particle. Fair enough, but here again the torque is given as relative to the origin, which really makes no sense to me, since the particle in question is not revolving about the origin, but rather around the z-axis (when torque was introduced in 2-D space, it was calculated relative to the point around which the body was rotating, which made sense). I try to accept this 'new' notion of torque as applied to a 3-D body, but can't, since it seems to me to imply the following: consider a solid cylinder rotating around the z-axis, with the base of the cylinder lying on the x-y plane. Now consider that I apply a tangential force somewhere on the surface of cylinder, in order to create rotational acceleration around the z-axis. According to the definition of torque as relative to the origin, the higher up on the cylinder that I apply the force, the greater the magnitude of [tex]\vec{r}[/tex], and thus the greater the magnitude of torque, which doesn't make sense to me.
Anyway, at this point the text goes on to confuse me further, but before we go there I'd like to resolve my confusion about the above. Any advice that might help me think through this a little more clearly? Thanks in advance!
Cheers,
Zain
The text begins by referring to an arbitrary 3-D rigid body rotating around the z-axis. This same body was used to discuss rotational energy, inertial moment calculation, etc. The text then considers one arbitrary particle of the body, and defines the angular momentum of the particle as [tex]\vec{r}[/tex] x m[tex]\vec{v}[/tex]. What's immediately odd to me about this is that [tex]\vec{r}[/tex] is considered relative to the origin of the coordinate system, when in previous sections it had been given as relative to the axis of rotation. Annoyed , I accept this and move on, but...
...Then the notion is introduced that the rate of change of this particle's angular momentum is equal to the torque applied to the particle. Fair enough, but here again the torque is given as relative to the origin, which really makes no sense to me, since the particle in question is not revolving about the origin, but rather around the z-axis (when torque was introduced in 2-D space, it was calculated relative to the point around which the body was rotating, which made sense). I try to accept this 'new' notion of torque as applied to a 3-D body, but can't, since it seems to me to imply the following: consider a solid cylinder rotating around the z-axis, with the base of the cylinder lying on the x-y plane. Now consider that I apply a tangential force somewhere on the surface of cylinder, in order to create rotational acceleration around the z-axis. According to the definition of torque as relative to the origin, the higher up on the cylinder that I apply the force, the greater the magnitude of [tex]\vec{r}[/tex], and thus the greater the magnitude of torque, which doesn't make sense to me.
Anyway, at this point the text goes on to confuse me further, but before we go there I'd like to resolve my confusion about the above. Any advice that might help me think through this a little more clearly? Thanks in advance!
Cheers,
Zain