What is angular velocity and radial velocity?
Angular velocity is the rate of change of angle of a body, i.e.
omega =
v / r =
(2*pi*r)/ r*t
=
(2*pi)/ T
where T is the time period of whatever is rotating and r is the radius of the circle.
So if a circular disc is spinning at 1 m/s then the angular velocity of it is 2*pi radians/ second
Radial velocity is the velocity in m/s at the radius of the circle i.e.
radial velocity v =
omega*r
=
(2*pi*r)/ T
(equivalent to speed =
distance/ time where in this case distance is the circumference of the circle and time is the time period of one rotation)
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Angular velocity ω, i
s the rate of change of angular displacement dφ
/dt
. Itspecifies the angular speed (rotational speed) of an object and the axis about which the object is rotating.
ω =
2
πf
=2
π/T [=]
rad/s
where f is the rotation frequency (rev/s) and T the time it takes to make a
revolution (s/rev).
Tangential velocity v. When an object rotates around in a circle with radius r, its
linear velocity tangent to the circle is the tangent velocity v.
v =
ωr
[=]
m/s
Radial velocity vr, is the component of the velocity of an object away or
toward
the origin or point of observation.
When you observe an object moving in a circle what can you infer about the net force acting on it?
The net force is directed toward the center of the circular path that the object is moving along, and it has a magnitude equal to the velocity squared times mass divided by the radius of the path. (mv^2/r)
Is centripetal force is acting when ab body is moving in stright line?
No, centripetal force is not acting when a body is moving in a straight line. Centripetal force is required to keep an object moving in a curved path.
Yes, suppose a body is rotating anti-clockwise, then its angular velocity and angular momentum, at any moment are along axis of rotation in upward direction. And when body is rotating clockwise, its angular velocity and angular momentum are along axis of rotation in downward direction. This is regardless of the fact whether angular velocity of the body is increasing or decreasing.
Is acceleration uniform in uniformly circular motion?
No, acceleration is not uniform in uniformly circular motion. In uniformly circular motion, the direction of the velocity vector is constantly changing, which means there is always a centripetal acceleration acting towards the center of the circle. This centripetal acceleration is not constant in magnitude, making the overall acceleration not uniform.
What is the relation between stiffness and angular velocity?
The stiffness of a system affects how it resists deformation when a force is applied. As angular velocity increases, the deformation of a system may change due to the increased speed at which the system is rotating. In some cases, an increase in angular velocity may lead to a decrease in stiffness as the system experiences greater deformation.
When driving when is centrifugal force a problem?
Centrifugal force can be a problem when taking sharp turns at high speeds, as it can cause the vehicle to lose traction and potentially skid off the road. This force is experienced when a vehicle is turning, pushing it outward from the center of the turn, which can lead to instability if not managed properly. It's important to adjust speed, brake before entering the turn, and steer smoothly to counteract centrifugal force.
Rotation motion occurs when an object spins around an axis, causing it to move in a circular path. This type of motion is commonly observed in objects such as wheels, planets, and rotating machinery. Rotation motion can be described in terms of angular velocity, which measures the rate of rotation.
Can small force exert greater torque?
Not exactly,torque is the force that affects rotational motion; the greater the torque, the greater the change in rotational motion. It is always specified with regard to the axis of rotation.
Derive equation between angular and linear acceleration?
Since angular acceleration is in radians per second squared, which is change in angular speed over time, we know that α=ω/t, where α is angular acceleration, ω is angular speed, and t is time (assuming α is constant.)
ω is measured in radians per second. If me multiply ω by r, which is the radius of the circle the object is acceleration around, we get ωr, which has units of (radians*radius)/second. Since the angle in radians times the radius gives the distance, these units are equivalent to meters/second, so ωr = v.
Therefore, α=(v/r)/t=v/rt.
Acceleration (a) is v/t, so α=(v/t)(1/r)=a/r.
The equation would then be:
α=a/r, or a=rα (Where α is angular acceleration, a is acceleration, and r is the radius.)
What is the Angular velocity of hour hand?
The angular velocity of the hour hand is 0.5 degrees per minute, because the hour hand completes a full rotation of 360 degrees in 12 hours.
Why is mass used to represent inertia?
Because after much investigation, experiment, and experience, in laboratories
of Physics all over the world, it has been determined that there is more inertia
where there is more mass, and less inertia where there is less mass. Moreover,
through careful measurement, it has been possible to quantify the relationship,
and to demonstrate, analytically and conclusively, that intertia is precisely and
directly proportional to mass, and that where there is no mass, inertia is zero.
Be that as it may, and when all is said and done, it became clear that mass is
like unto no other quantity as a worthy and proper surrogate for inertia.
The source of the centripetal force that keeps the child moving in a circle is tension in the rope or the father's grip. This force is directed towards the center of the circular motion and prevents the child from flying off tangentially. Gravity and weight also play a role in the overall forces acting on the child but are not the direct source of the centripetal force in this scenario.
Could the angular momentum of the closed system of mass change?
In a closed system where no external torque acts, the angular momentum remains constant (law of conservation of angular momentum). If external torques are present, the angular momentum of the system can change due to the torque causing rotation.
The energy that the object has when it's spinning is never "used up", unless
there's something acting on the object to rob energy from it. In our daily
experience on Earth, there's ALWAYS some friction acting on a spinning object.
The friction robs energy from it, and it eventually stops spinning. That's why
it's so hard for us to understand and accept Newton's law that tells us how
things REALLY work. An object in motion continues in motion unless it's acted
on by an external force. In other words, if something is moving, it doesn't take
any force or action to KEEP it moving. We just never see this happen on Earth,
because we can never set anything up WITHOUT any outside forces that act
to make it stop, so we always have to do something to keep it moving.
How does a centripetal force keep an object moving in a circle?
A centripetal force acts towards the center of the circle, continually changing the object's direction towards the center. This force prevents the object from moving in a straight line and keeps it moving in a circular path.
Can a body in translatory motion have angular momentum?
No, a body in translatory motion does not have angular momentum as angular momentum is associated with rotational motion. Translatory motion involves motion along a straight line, while angular momentum involves rotation around an axis.
What is the formula for the centripetal acceleration force of a mass?
The formula for centripetal acceleration is a = v^2 / r, where a is the centripetal acceleration, v is the velocity of the object, and r is the radius of the circular path. The force required to produce this acceleration is given by F = m * a, where F is the centripetal force, m is the mass of the object, and a is the centripetal acceleration.
Why does a skater angular velocity increase when putting their arms in?
the equation for rotational kinetic energy (KE) is:
.
KE = 0.5 * I * ((rad / sec)^2), where I is the mass moment of inertia.
.
so if the kinetic energy remains constant, the only thing that can alter the rotation rate (rad / sec), is I, the mass moment of inertia
What causes centrifugal force?
Centrifugal force is not a real force, but rather an apparent outward force that arises in a rotating reference frame. It is a result of inertia and is experienced by objects moving in a circular path due to their inertia trying to move in a straight line, away from the center of rotation.
Can you explain centripetal force?
Centripetal force is a force that makes a body follow a curved path: it is always directed orthogonal to the velocity of the body, toward the instantaneous center of curvature of the path.
I linked my source.
In what units is Angular acceleration expressed?
Angular acceleration is typically expressed in units of radians per second squared (rad/s^2).
Does the blade of a fan that is turned on have angular momentum?
Yes, the blade of a fan that is turned on does have angular momentum because it is rotating around an axis. The angular momentum depends on the rotational speed of the blade and its moment of inertia.
How do force and torque work in the human body?
Force is used to create movement in the human body, such as when muscles contract to move a limb. Torque, on the other hand, refers to the rotational force created when a force is applied at a distance from a pivot point, such as when throwing a ball or lifting a weight. Both force and torque are essential for various movements and functions in the human body.
What is the Conditions for angular acceleration equal to zero?
Angular acceleration is equal to zero when an object is rotating at a constant angular velocity without any change in its rotational speed. This occurs when the net torque acting on the object is zero, meaning that there are no external forces causing the object to accelerate or decelerate rotationally.