Description of Work, energy and motion

Uniform Circular Motion

(1)Velocity is continiously changing as the direction of velocity is changing. The Speed of the mass remains constant (speed = |velocity|)
2. The centripetal force is keeping the mass in its path and is given by, F = mv^2/R
3. If a mass m tied to the end of a string is whirled in a vertical circle, the tension in the string wiil be max at the bottom and minimum at the top

T = centripetal force - mg (min)

4. Tangential acceleration is zero in UNIFORM circular motion
5. Radial acceleration (acting towards the radius) is not zero. V^2/R

Potential energy

The energy of a body by virtue of its postion (height):
it is always given by mass*g*height = mgh
This is the work done by you in bringing the body at this height. It gets stored in the body as it PE.
when a body falls down, at the bottom point this much energy is converted to its KE so that total energy remains constant.

at the bottom we can write, mgh = (1/2)mv^2

The total energy = KE + PE remains constant for all bodies
KE = (1/2)mv^2 and PE = mgh

you can apply this to a variety of problems.

KE1 + PE1 = KE2+ PE2

Where you can substitute for values of v and h at different points and find the height or velocity at the other point.

Work done by any force is the dot product (F.ds) of the force vector and the displacement vector.

F.ds = F*ds*Cos(theta)

Newton's law:

If you found a velocity change for a mass m in time t the applied force is F = m* dV/dt

where dv/dt = a, the acceleration (rate of change of velocity)

(dv/dt = v1-v2/time)

Every action has an equal and opposite reaction: This is sometimes referred to as the weak law of action and reaction.

Please read your text carefully, evenif you know the equations you may not be able to do the problem you must try to understand what the problem is asking you. Try to read the question two or three times.

Wish you all the best.

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