Rotational kinematics of a ball

In summary, rotational kinematics is the study of the motion of objects in a circular path, taking into account concepts such as displacement, velocity, and acceleration. It differs from linear kinematics and involves measuring angular displacement and linear displacement. The radius of a circle affects rotational kinematics by influencing the angular displacement, velocity, and acceleration of an object. It is applied in various real-life situations, including sports, engineering, and the motion of objects such as planets and wheels.
  • #1
medicle
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0

Homework Statement



A ball attached to a string starts at rest and undergoes a constant angular acceleration as it
travels in a horizontal circle of radius 0.30 m. After 0.65 sec, the angular speed of the ball is 9.7
rad/s. Determine the magnitudes of the ball’s tangential, centripetal, and total acceleration at
t = 0.30 s.


Homework Equations





The Attempt at a Solution


at=w-wo/t = 9.7/.65 =15 15(.30)=4.5m/s^2

which is correct. for ac I did 9.7/.3= 32.3 32.3(.65)= 21 21(.3)= 6.3


Is this correct?

NOt sure were to start for a?

Any help would be awesome.
 
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never mind
 

FAQ: Rotational kinematics of a ball

What is rotational kinematics?

Rotational kinematics is the study of the motion of objects that are rotating or moving in a circular path. It involves understanding the concepts of displacement, velocity, and acceleration in relation to rotational motion.

How is rotational kinematics different from linear kinematics?

Rotational kinematics is different from linear kinematics because it involves the motion of objects in a circular path, while linear kinematics deals with motion in a straight line. This means that rotational kinematics takes into account the angular displacement, angular velocity, and angular acceleration of an object, which are not present in linear kinematics.

What is the difference between angular displacement and linear displacement?

Angular displacement measures the change in the angle of rotation of an object, while linear displacement measures the change in the position of an object in a straight line. Angular displacement is measured in radians, while linear displacement is measured in meters.

How does the radius of a circle affect rotational kinematics?

The radius of a circle is directly related to the angular displacement, velocity, and acceleration of an object in rotational motion. A larger radius will result in a larger angular displacement for the same linear displacement, and a smaller angular velocity for the same linear velocity. It also affects the centripetal acceleration of an object, as a larger radius will result in a smaller centripetal acceleration.

How is rotational kinematics applied in real-life situations?

Rotational kinematics is used in many real-life situations such as the motion of wheels on a car, the spinning of a top, and the motion of planets around the sun. It is also used in sports such as golf and baseball, where understanding the rotational motion of a ball is important for achieving accurate shots. Additionally, rotational kinematics is used in engineering to design machines that involve rotational motion, such as turbines and motors.

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