PHYSICS

• Fixed axis - a line perpendicular to the plane of the object and passing

  through the center of the rotating body at O
• Arbitrary particle- any small element of the body.
• radius - distance of particle P from the origin O.
• Angular position - is the angle measured counterclockwise from some reference line.
• Polar coordinates - represents the angular position of particle P
• Arc length - is the distance travelled by a particle along a circle of radius r
• Angular position - It is defined as the arc length s along a circle divided by the radius r
• Conversion of units

  2π rad = 360° = 1 rev
• Angular Displacement - defined as the angle the object rotates about the fixed axis at a given time interval.
• Positive if the disc is rotating in counter-clockwise direction.
• Negative if the disc is rotating in clockwise direction.
• Average Angular velocity - the ratio of the angular displacement to the time interval
• Instantaneous Angular velocity - is defined as the limit of the average speed as the time interval approaches zero
• Angular velocity,ω

  • Speed is positive if θ is increasing (counterclockwise). The thumb is pointing out of the page (+z – axis).

  • Speed is negative if θ is decreasing (counterclockwise). The thumb is

  pointing into the page (-z – axis).
• Average Angular Acceleration - is the rate of change of the angular speed of object ∆ω during time interval Δt.
• The instantaneous angular acceleration is the limit of the average acceleration as the time interval approaches zero
• Tangential Velocity is defined as the distance traveled by a particle P measured along the circular path in a given time interval.
• Tangential Velocity is always tangent to the circular path.
• Tangential Velocity varies as the radius r varies.
• Tangential Acceleration is defined as the translational acceleration of a point on rotating rigid object equals to the radius r multiplied by the angular acceleration.
• radial Acceleration is defined as the acceleration due to the change in the direction of the tangential velocity which is directed toward the center of rotation.
• The Total Acceleration of a particle on the rotating rigid body is defined as the resultant acceleration of the tangential and radial accelerations.
• The direction of the tangential acceleration is always perpendicular to the radius of the rotation.
• If the rotating body decelerates, the directions of its rotation and its acceleration is opposite
• The torque of a force is maximum when it is acting perpendicular at a distance from a fulcrum.
• The torque of a force is positive when it tends the object to rotate counterclockwise.
• Torque is a vector quantity.
• Centripetal acceleration is the other term for radial acceleration.
• The magnitude of the lever arm is directly proportional to the magnitude of the torque.
• The tangential velocity is the measure of the arc length travelled by a particle per unit of time.
• Center of gravity is always located on the geometric confines of the object regardless of the shape.
• Torque causes angular accelerations
• Torque is the tendency of a force to rotate an object about some axis
• If the turning tendency of the force is counterclockwise, the torque will be positive
• If the turning tendency is clockwise, the torque will be negative
• Direction of torque - the direction is perpendicular to the plane determined by the position vector and the force
• When two or more torques are acting on an object, the torques are added as vectors
• If the net torque is zero, the object’s rate of rotation doesn’t change
• The applied force is not always perpendicular to the position vector.
• The component of the force perpendicular to the object will cause it to rotate