A hockey puck of mass m = 0.25 kg is tied to a string and is rotating horizontally in a
circle of radius R = 1.0 m on top of a frictionless table.
The mass of the puck does not affect its rotational motion in a circular path, only the force required to keep it in that path. The mass of the puck is the same whether it is rotating or not. The force keeping the puck in a circular path is provided by the tension in the string, which is determined by the speed of rotation and the mass of the puck.
A hockey puck of mass m = 0.25 kg is tied to a string and is rotating horizontally in a circle of radius R = 1.0 m on top of a frictionless table. The string is passing through a hole in the center of the table with a mass of 1 kg hanging vertically downward below the table. If the 1 kg mass hanging below the table remains in equilibrium (at a fixed position) while the puck is rotating horizontally. Since the weight below the table remains in equilibrium, the tension in the rope must equal the weight suspended from it T = W = (1 kg) × (9.81 m/s2 ) = 9.81 N
A ball at the end of a 0.75 m string rotating at constant speed in a circle has an angular velocity of (2 pi) divided by (time to complete one revolution). Time to complete one revolution = (speed) divided by (2 times pi times radius). If you write this algebraically and then simplify the fraction, you find that the angular velocity is (4 times pi2 times radius) divided by (speed) = (29.609/speed) radians/sec. The speed is expressed in meters/sec. The solution doesn't depend on the orientation of the plane of the circle.
The tension in the string would increase as it is being stretched, causing the string to become tighter. The frequency at which the string vibrates would also increase, resulting in a higher pitch when plucked.
In a stretched string, the center of gravity refers to the point where the force of gravity can be considered to act on the entire string. It is typically located at the midpoint of the string's length when the string is held horizontally. This point helps determine how the string will behave under the influence of gravity and other external forces.
The mass of the puck does not affect its rotational motion in a circular path, only the force required to keep it in that path. The mass of the puck is the same whether it is rotating or not. The force keeping the puck in a circular path is provided by the tension in the string, which is determined by the speed of rotation and the mass of the puck.
A hockey puck of mass m = 0.25 kg is tied to a string and is rotating horizontally in a circle of radius R = 1.0 m on top of a frictionless table. The string is passing through a hole in the center of the table with a mass of 1 kg hanging vertically downward below the table. If the 1 kg mass hanging below the table remains in equilibrium (at a fixed position) while the puck is rotating horizontally. Since the weight below the table remains in equilibrium, the tension in the rope must equal the weight suspended from it T = W = (1 kg) × (9.81 m/s2 ) = 9.81 N
Loop the string around the thumbtack and the pencil so that the distance from the tack to the pencil point is AB units. Fix the thumbtack to where you want the centre of the circle. Using the pencil, and with the string taut, mark its positions. These will lie on a circle with radius AB.
The circumference is the length of the outside of the circle. For example, if you took a piece of string and made a circle with it, then laid the string straight, the length of the string would be the circumference. The circumference of a circle can be measured by doing two times the radius of the circle times the mathematical constant, pi.
public class CircleDiameter { publicCircleDiameter() { super(); } publicfloatgetDiameterFrmRadius(float radius){ return radius * 2; } /** * @param args */ public static void main(String[] args) { float radius = 5; CircleDiameter circle = newCircleDiameter(); float dia = circle.getDiameterFrmRadius(radius); System.out.println("Diameter of this circle is: " + dia); } }
A ball at the end of a 0.75 m string rotating at constant speed in a circle has an angular velocity of (2 pi) divided by (time to complete one revolution). Time to complete one revolution = (speed) divided by (2 times pi times radius). If you write this algebraically and then simplify the fraction, you find that the angular velocity is (4 times pi2 times radius) divided by (speed) = (29.609/speed) radians/sec. The speed is expressed in meters/sec. The solution doesn't depend on the orientation of the plane of the circle.
15.8 m/s
If you want an approximate answer, you can measure it with string. If you want an exact answer and know the radius, multiply by 2*pi to find the circumference.
inward
If a ball swinging in a circle on a string is moved twice as fast, the tension in the string, which provides the centripetal force, will increase. The centripetal force required is proportional to the square of the velocity; thus, if the speed doubles, the force will increase by a factor of four. This relationship is described by the formula ( F = \frac{mv^2}{r} ), where ( m ) is the mass of the ball, ( v ) is the velocity, and ( r ) is the radius of the circle. Therefore, the force of the string will be four times greater.
it's a loop
Put a peg in the ground where you want the centre of the circle. Tie a string to the peg - loose enough so tat the string is free to rotate around the peg. Measure 5 metres along the string, from the peg, and at that point tie something that will mark the ground - a stick, for example. Walk around the central peg, holding the stick to the ground and keeping the string taut.