Embedded Files
Angular Acceleration is the rate of change of angular velocity
β πΌ = π₯π€/π₯π‘
β If w increases, alpha is positive
β If w decreases, alpha is negative
β Its units are (rad/s)/s
Tangential Acceleration is the acceleration in a direction tangent to the circle at the point of interest in circular motion
β It refers to changes in the magnitude of velocity but not its direction
β It is perpendicular and independent to centripetal acceleration
β It is instead directly related to angular acceleration
β πΌ = πt/π
β It is also linked to an increase or decrease in the velocity, but not its direction
The kinematics of rotational motion describe the relationships among rotation angle, angular velocity, angular acceleration, and time
β π = π€π‘
β π€ = π€0 + πΌπ‘
β π = π€0t + .5πΌπ‘2
β π€2 = π€20 + 2πΌπ
These are the steps to take for rotational kinematics problems:
β Examine the situation to determine that rotational kinematics are involved
β Identify exactly what needs to be determined in the problem
β Draw a sketch of the situation
β Make a list of what is given or can be inferred from the problem as stated
β Solve the appropriate equation or equations for the quantity to be determined
β Substitute the known values along with their units into the appropriate equation
β Obtain numerical solutions complete with units
β Check your answer to see if it is reasonable
The moment of inertia is the mass times the square of perpendicular distance from the rotation axis
β πΌ = ππ2
β I is analogous to m in translational motion
β So, net π = πΌπΌ
β The larger the torque, the larger the angular acceleration
β Distribution of mass relative to the axis around which it rotates also plays a part
These are the steps to take for rotational dynamics problems:
β Examine the situation to determine that torque and mass are involved in the rotation
β Draw a sketch of the situation
β Determine the system of interest
β Draw a free body diagram
β Draw and label all external forces acting on the system of interest
β Apply net π = πΌπΌ to solve the problem
β Check the solution to see if it is reasonable
Rotational kinetic energy is the kinetic energy due to the rotation of an object
β Netπ = (πππ‘ π)π
β πΎπΈrot = .5πΌπ€2
These are the steps to take for rotational energy problems:
β Determine that energy or work is involved in the rotation
β Determine the system of interest
β Draw a sketch of the situation
β Analyze the situation to determine the types of work and energy involved
β For closed systems, mechanical energy is conserved
β Kinetic energy may include translational and rotational contributions
β For open systems, mechanical energy may not be conserved
β Other forms of energy may enter or leave the system (heat)
β Determine what they are, and calculate them as necessary
β Eliminate terms wherever possible to simplify the algebra
β Check the answer to see if it is reasonable
Angular momentum is the product of moment of inertia and angular velocity
β πΏ = πΌπ€
β An object that has a large moment of inertia has a large angular momentum
β An object that has a large angular velocity has a large angular momentum
β Net π = π₯πΏ/π₯π‘
β If the torque you exert is greater than opposing torques, then the rotation accelerates, and angular momentum increases
The law of conservation of angular momentum states that the initial angular momentum is equal to the final angular momentum when no external torque is applied to the system.
β πΏ = πΏβ²
β πΌπ€ = πΌβ²π€β²
Page updated
Google Sites
Report abuse