Phy201
Your 'cq_1_25.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** **
A steel ball of mass 110 grams moves with a speed of 30 cm / second around a circle of radius 20 cm.
• What are the magnitude and direction of the centripetal acceleration of the ball?
answer/question/discussion:
a = v^2/r = (30 cm/s)^2/20 cm = 45 cm/s^2 or .45 m
45 cm/s^2 is correct.
However 45 cm/s^2 is not the same as .45 m. Among other things, the first has units of length / time^2, while the second has units of just length.
You probably meant .45 m/s^2, which would be equivalent to your first answer.
F = m * a = .11 kg * .45 m = .05 Newtons
kg * m will not give you Newtons.
.05 Newtons is the correct answer here, but because of the units it does not result from the calculation you have given.
According to the Asst 24 start q a, the direction of the centripetal motion is to the center of the circle. I’m sure if that is what is being asked. I would think that the motion or direction would be in a circular direction.
The angular velocity here is constant, so if the motion can be represented by a vector, it has to be represented by a single vector.
What single vector points in a circular direction?
Think about it then see my answer at the end.
• What is the magnitude and direction of the centripetal force required to keep it moving around this circle?
answer/question/discussion:
The magnitude is .05 Newtons and the direction of the centripetal force is toward the center of the circle.
** **
about 10 minutes while conferring with asst 24 start q a lesson
** **
Good work, but be sure to see my notes, especially as related to an error you made in units.
The answer to the question about direction of centripetal motion (see my note above before you look at this answer):
Motion in a circle consists of motion about a single axis through the center. The axis is perpendicular to the plane of the circle.
There are two directions parallel to this axis. One of the directions is found by 'wrapping' your right hand around the circle, with your fingers pointing around the circle in the same sense as the motion of the object. Your thumb will point in a direction along the axis. Take this as the direction of the vector that describes the motion.
As you will see later, there is a good reason for this rule, and it helps us to understand the behavior of bicycle wheels, gyroscopes, and similar systems.