1) The position vector of a particle is r= (a cosώt) i+ (a sinώt) j. The velocity of the particle is and find the parallel position vector.
No, uniform angular velocity means no angular acceleration.
Angular acceleration is the trate of change of angular velocity, often represented by the letter alpha.
The direction of angular acceleration comes from whether the angular speed of the object is clockwise or counterclockwise and whether it is speeding up or slowing down.The direction of the angular acceleration will be positive if the angular velocity is counterclockwise and the object's rotation is speeding up or if the angular velocity is clockwise and the object's rotation is slowing downThe direction of the angular acceleration will be negative if the angular velocity is clockwise and the object's rotation is speeding up or if the angular velocity is counterclockwise and the object's rotation is slowing downThe angular acceleration will not have a direction if the object's angular velocity is constant
Assuming that angles are measured in radians, and angular velocity in radians per second (this simplifies formulae): Radius of rotation is unrelated to angular velocity. Linear velocity = angular velocity x radius Centripetal acceleration = velocity squared / radius Centripetal acceleration = (angular velocity) squared x radius Centripetal force = mass x acceleration = mass x (angular velocity) squared x radius
The rate of change of velocity is known as acceleration. This can come in different forms (linear / nonlinear acceleration, angular acceleration ect).
No, uniform angular velocity means no angular acceleration.
Angular acceleration is the trate of change of angular velocity, often represented by the letter alpha.
Take the velocity to be in positive direction. Positive acceleration increases velocity and they are in the same direction. Negative acceleration reduce velocity and they are in opposite direction. It does not matter if the motion in linear or anfular.
The direction of angular acceleration comes from whether the angular speed of the object is clockwise or counterclockwise and whether it is speeding up or slowing down.The direction of the angular acceleration will be positive if the angular velocity is counterclockwise and the object's rotation is speeding up or if the angular velocity is clockwise and the object's rotation is slowing downThe direction of the angular acceleration will be negative if the angular velocity is clockwise and the object's rotation is speeding up or if the angular velocity is counterclockwise and the object's rotation is slowing downThe angular acceleration will not have a direction if the object's angular velocity is constant
Assuming that angles are measured in radians, and angular velocity in radians per second (this simplifies formulae): Radius of rotation is unrelated to angular velocity. Linear velocity = angular velocity x radius Centripetal acceleration = velocity squared / radius Centripetal acceleration = (angular velocity) squared x radius Centripetal force = mass x acceleration = mass x (angular velocity) squared x radius
momentum is product of moment of inertia and angular velocity. There is always a 90 degree phase difference between velocity and acceleration vector in circular motion therefore angular momentum and acceleration can never be parallel
Angular velocity just means how fast it's rotating. If youaa want more angular velocity, just rotate it faster or decrease the radius (move it closer to the center of rotation). Just like force = rate of change of momentum, you have torque= rate of change of angular moment Or We can increase the angular velocity of a rotating particle by applying a tangential force(i.e. accelaration) on the particle. Since the velocity of the particle is tangential with the circle along which it is moving, the tangential accelaration will not change the diriction of the velocity(as angle is 0),but will cause a change in magnitude. Thus angular velocity will increase.
Centrifugal governors respond to angular velocity. Inertia governors respond to angular acceleration.
The rate of change of velocity is known as acceleration. This can come in different forms (linear / nonlinear acceleration, angular acceleration ect).
a=(v^2)/r or a=r(angular velocity)^2
angular momentum and angular velocity
It was 6 radians per second. Angular acceleration = -3 radians per second2 Initial angular velocity = 6 radians per second. Final angular velocity = zero. Average angular velocity = 3 radians per second. Angular displacement in 2 seconds = 3 x 2 = 6 radians.