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What does the linear speed of a rotating object depend on?
The linear speed of a rotating object depends on its angular speed (how fast it rotates) and the distance from the axis of rotation (the radius). Linear speed is calculated as the product of the angular speed and the radius.
Relation between linear speed and angular velocity?
Linear speed is directly proportional to the radius of rotation and the angular velocity. The equation that relates linear speed (v), angular velocity (ω), and radius (r) is v = rω. This means that the linear speed increases as either the angular velocity or the radius of rotation increases.
If the radius of rotation and the mass being kept constant how does centripetal force vary with the speed of rotation body?
Centripetal force is directly proportional to the square of the speed of rotation. As the speed of rotation increases, the centripetal force required to keep the object moving in a circular path also increases. This relationship follows the formula Fc = mv^2 / r, where Fc is the centripetal force, m is the mass, v is the speed, and r is the radius of rotation.
How does change in radius effect the linear speed?
The linear speed is directly proportional to the radius of rotation. An increase in radius will result in an increase in linear speed, while a decrease in radius will result in a decrease in linear speed. This relationship is governed by the equation v = ω * r, where v is linear speed, ω is angular velocity, and r is radius.
Centrifugal force increases with?
Centrifugal force increases with increasing speed and radius of rotation. The faster an object moves in a circular path or the larger the radius of rotation, the stronger the centrifugal force acting on the object.
What does the linear speed of a rotating object depend on?
The linear speed of a rotating object depends on its angular speed (how fast it rotates) and the distance from the axis of rotation (the radius). Linear speed is calculated as the product of the angular speed and the radius.
Relation between linear speed and angular velocity?
Linear speed is directly proportional to the radius of rotation and the angular velocity. The equation that relates linear speed (v), angular velocity (ω), and radius (r) is v = rω. This means that the linear speed increases as either the angular velocity or the radius of rotation increases.
If the radius of rotation and the mass being kept constant how does centripetal force vary with the speed of rotation body?
Centripetal force is directly proportional to the square of the speed of rotation. As the speed of rotation increases, the centripetal force required to keep the object moving in a circular path also increases. This relationship follows the formula Fc = mv^2 / r, where Fc is the centripetal force, m is the mass, v is the speed, and r is the radius of rotation.
How does change in radius effect the linear speed?
The linear speed is directly proportional to the radius of rotation. An increase in radius will result in an increase in linear speed, while a decrease in radius will result in a decrease in linear speed. This relationship is governed by the equation v = ω * r, where v is linear speed, ω is angular velocity, and r is radius.
Centrifugal force increases with?
Centrifugal force increases with increasing speed and radius of rotation. The faster an object moves in a circular path or the larger the radius of rotation, the stronger the centrifugal force acting on the object.
What happens to the number of revolutions of a rubber stopper as the radius of rotation decreases?
As the radius of rotation decreases, the number of revolutions of a rubber stopper increases. This is due to the conservation of angular momentum - with a smaller radius, the rotational speed must increase to maintain the same angular momentum.
If the radius of rotation and the mass being kept constant how does the centripetal force vary with the speed of rotation of the body?
Recall centripetal force = m v^2 / rAs m and r are found to be constants then centripetal force F is directly proportional to the square of the velocity of the body
What is the speed of a point on the rim of an object in motion?
The speed of a point on the rim of an object in motion is determined by the object's rotational speed and the distance of the point from the center of rotation. This speed is calculated using the formula: speed radius x angular velocity.
Does the center of circle turn at the double speed as the outside if radius is double?
The centre of the circle does not turn at all: the axis of rotation goes through it.
How does the centripetal force with the speed of rotation of the body with constant mass and radius of rotation?
You can calculate the centripetal ACCELERATION with one of these formulae: acceleration = velocity squared / radius acceleration = omega squared x radius Acceleration refers to the magnitude of the acceleration; the direction is towards the center. Omega is the angular speed, in radians per second. To get the centripetal FORCE, you can use Newton's Second Law. In other words, just multiply the acceleration by the mass.
What is the formula for rotation in math?
In 2-dimensions, the formula for rotation through d degrees is [post-]multiplication by the matrix [cos(d) sin(d)] [-sin(d) cos(d)]
Why is the centrifugal acceleration decrease from the equator to the poles?
The relevant formula here is:centrifugal acceleration = omega squared x radiusomega (the angular speed) doesn't change in this formula (for the situation under consideration), but "radius", the distance from the axis of rotation, does.
