Help with physics homework?

Question

What is a) the force necessary to keep a ball of mass 1 kg travelling in a circle of raduis 1 meter at a speed of 1 m/s? b) the angular velocity of the ball? c) the kinetic energy of the ball?


Any help would be greatly appreciated :-)!!!

Answer 1

1) That would be the centripetal force, given by (m v^2)/r. Just plug in.

2) Probably the easiest way to get this one is to realize that the ball is travelling along the circumference of a circle of radius 1 m. The circumference of a circle is 2 pi r. It's travelling at 1 m/s, so the period (the time it takes to go around once) will be (2 pi r)/v = 2 pi r seconds. Take the reciprocal and multiply by 2 pi radians in one circle and you'll have the angular speed, which will work out to v/r = 1(m/s)/1 m = 1 s^-1. You don't have enough information to get the angular velocity, but I suspect it's the speed that's required.

3) You know the mass and speed of the ball. Just use T = (1/2) m v^2.

Answer 2

Consider a free body diagram of the ball. What are the forces on the ball?

There is a force that keeps the ball traveling in a circle. That force is radial with respect to the center of the circle.

F=m*w^2*r
Where w is the angular velocity equal to v/r

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