# Homework Help: Uniform Circ. Motion, Only Accel Given.

1. Oct 7, 2006

### intelligentDesign

Hello All, I am trying to figure out this problem, and any help would be great!

A Penguin moves in counterclockwise uniform circular motion. At one instant, it's centripetal acceleration (in m/s^2) is 6i + 4j. Three seconds later, the centripetal acceleration is 4i-6j.
A. What is the penguin's period?
B. What is the radius of the penguin's motion?
C. What is the penguin's speed?

I converted the unit vector forms into maginitude direction form, and found out, suppposing that in three seconds, the penguin did not complete a revolution, the period is four seconds.
But now I am trying to figure out the rest.
Sorry to be so arbitrary, but any hints?
Thanks!
Murphy :surprised

2. Oct 7, 2006

### arildno

Well, you know the period of the penguin, hence you know its angular velocity!
B. Thus, how is angular velocity, radius and magnitude of centripetal acceleration related to each other?

C. How is radius, angular velocity and linear speed related to each other?

3. Oct 7, 2006

### intelligentDesign

Hmm,
One quesiton, what is angular velocity? is it different than insntantaneous velocity?
how do I find the angular velocity by knowing the period?

B) A = (V^2)/r

C)Well, I know that speed (magnitude of velicoity) is constant, although the direction of the velocity is constantly changing to be tangent to the edge of the circle. and I know that the radius is the distance of the penguin from the center?

Thanks!

P.S. sorry! just saw the sticky about not posting homework questions here.
Thanks again!

4. Oct 7, 2006

### arildno

Angular velocity is angular displacement divided with time.
Since a full revolution equals 2*pi, and the period T is just the time needed to complete a cycle, the angular velocity is simply w=2*pi/T

5. Oct 7, 2006

No, there can be instantaneous angular velocity defined as $$lim_{\Delta t \rightarrow 0}\frac{\theta(t + \Delta t)-\theta(t)}{\Delta t}=\omega$$.

6. Oct 7, 2006

### intelligentDesign

Wow, thanks!
what's the differance between angular velocity, and velocity?
or angluar displacement and displacement?

7. Oct 7, 2006

Angular velocity is used to define rotation of a straight line around a fixed point.

8. Oct 7, 2006

### jalaldn

in physics, quantitative measure of the rotational inertia of a body—i.e., the opposition that the body exhibits to having its speed of rotation about an axis altered by the application of a torque (turning force). The axis may be internal or external and may or may not be fixed. The moment of inertia (I), however, is always specified with respect to that axis and is defined as the sum of the products obtained by multiplying the mass of each particle of matter in a given body by the square of its distance from the axis. The figure shows two steel balls that are welded to a rod AB that is attached to a bar OQ at C. Neglecting the mass of AB and assuming that all particles of the mass m of each ball are concentrated at a distance r from OQ, the moment of inertia is given by I = 2mr2.

The unit of moment of inertia is a composite unit of measure. In the International System (SI), m is expressed in kilograms and r in metres, with I (moment of inertia) having the dimension kilogram-metre square. In the U.S. customary system, m is in slugs (1 slug = 32.2 pounds) and r in feet, with I expressed in terms of slug-foot square.

The moment of inertia of any body having a shape that can be described by a mathematical formula is commonly calculated by the integral calculus. The moment of inertia of the disk in the figure about OQ could be approximated by cutting it into a number of thin concentric rings, finding their masses, multiplying the masses by the squares of their distances from OQ, and adding up these products. Using the integral calculus, the summation process is carried out automatically; the answer is I = (mR2)/2.

For a body with a mathematically indescribable shape, the moment of inertia can be obtained by experiment. One of the experimental procedures employs the relation between the period (time) of oscillation of a torsion pendulum and the moment of inertia of the suspended mass. If the disk in the figure were suspended by a wire OC fixed at O, it would oscillate about OC if twisted and released. The time for one complete oscillation would depend on the stiffness of the wire and the moment of inertia of the disk; the larger the inertia, the longer the time.

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