Force in Circular Motion

FORCE IN CIRCULAR MOTION

Uniform Circular Motion refers to a motion along a circular path with a uniform speed but constantly changing direction. It is accelerated motion.

Frequency (f) = Refers to the number of complete revolutions per unit of time.

Centripetal acceleration (central acceleration) = it is primarily acts at right angles to its velocity.

Central Force = refers to the force that compels a body to move toward the center.

* If the mass is doubled, the force is also doubled, but doubling the speed will increase the force four times. If the radius is doubled, this will decrease the force twice as much.

Period (τ) is define as the time for one revolution and often stated as the reciprocal of frequency (1 / f).

Angular velocity refers to the rate of angular displacement. The rate of angular turned through.

* the direction of the velocity is always tangent to the circular path.

* radian as the unit of angle

Linear velocity is the product of angular velocity and its radius. V = r ω

Sample Problem:

1. If the radius of the circular path of a stone is 0.5m and its period is 0.5 sec, what is its constant speed?

2. What is the angular and linear velocity of a stone which makes 10 rev in 5 sec? The radius of the circular path is 0.5 m. First find the angle of turned through

3. Half kilogram mass is whirled in a horizontal circle of radius 2m. If it makes 5 revolutions in 5 seconds, find its (a.) constant speed, (b.) central acceleration and (c.) central force.

4. Find the central force required by a Hammer car ( mass, 3000kg) that round a curve of radius 35m at a speed of 8 m/s.

5. A mass of 2 kg is moving in a horizontal circle of 1m radius with an angular velocity of 3 rad/s. What is the required central force?

6. A 50 gram body fastened to one end of a string 0.75m long, is made to move with uniform circular motion at 3 revolutions per second on a smooth horizontal surface, with one end of the string as its center, find (a.) the speed of the body and (b.) the central force

7. A small plastic box mass 0.200kg revolves uniformly in a circle on a frictionless horizontal surface such as an air hockey table. It is attached by a cord 0.200m long to a pin se in he surface. If the body makes two complete revolution per second, find the force F exerted on it by the cord.