1) Draw the free body force diagram. Use Newton’s second law and also the rotational version of Newton’s second law: Net Torque = I alpha , where I is the moment of inertia, and alpha is the angular acceleration. Using the two equations, derive a formula for the angular acceleration of the pulley in terms of I,m and r(and g). To get you started, note that: The torque acting on the pulley is caused by the weight of the pulling mass. That weight force, mg generates a torque of mgr on the pulley, about an axis running through its middle. The magnitude of the acceleration of the hanging mass is equal to the magnitude of the acceleration of the rim of the pulley. The tangential acceleration, a, of a rotating object at radius r from the axis of rotation can be written in terms of the angular acceleration as follows: a = r alpha
1) Draw the free body force diagram. Use Newton’s second law and also the rotational version of Newton’s second law: Net Torque = I alpha , where I is the moment of inertia, and alpha is the angular acceleration. Using the two equations, derive a formula for the angular acceleration of the pulley in terms of I,m and r(and g). To get you started, note that: The torque acting on the pulley is caused by the weight of the pulling mass. That weight force, mg generates a torque of mgr on the pulley, about an axis running through its middle. The magnitude of the acceleration of the hanging mass is equal to the magnitude of the acceleration of the rim of the pulley. The tangential acceleration, a, of a rotating object at radius r from the axis of rotation can be written in terms of the angular acceleration as follows: a = r alpha
1) Draw the free body force diagram. Use Newton’s second law and also the rotational version of Newton’s second law: Net Torque = I alpha , where I is the moment of inertia, and alpha is the angular acceleration. Using the two equations, derive a formula for the angular acceleration of the pulley in terms of I,m and r(and g). To get you started, note that: The torque acting on the pulley is caused by the weight of the pulling mass. That weight force, mg generates a torque of mgr on the pulley, about an axis running through its middle. The magnitude of the acceleration of the hanging mass is equal to the magnitude of the acceleration of the rim of the pulley. The tangential acceleration, a, of a rotating object at radius r from the axis of rotation can be written in terms of the angular acceleration as follows: a = r alpha
1) Draw the free body force diagram. Use Newton’s second law and also the rotational version of Newton’s second law: Net Torque = I alpha , where I is the moment of inertia, and alpha is the angular acceleration. Using the two equations, derive a formula for the angular acceleration of the pulley in terms of I,m and r(and g). To get you started, note that:
The torque acting on the pulley is caused by the weight of the pulling mass. That weight force, mg generates a torque of mgr on the pulley, about an axis running through its middle.
The magnitude of the acceleration of the hanging mass is equal to the magnitude of the acceleration of the rim of the pulley.
The tangential acceleration, a, of a rotating object at radius r from the axis of rotation can be written in terms of the angular acceleration as follows: a = r alpha
Transcribed Image Text:M, mass
of pulley
r, radius of
pulley
m,
pulling
mass
Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .
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