A pendulum consisting of a string of length L attached to a bob of mass m swings

Question

A pendulum consisting of a string of length L attached to a bob of mass m swings in a vertical plane.

(a) When the string is at an angle ? to the vertical, calculate the tangential acceleration of the bob.
(b) When the string is at an angle ? to the vertical, calculate the centripedal acceleration of the bob .
(c) What is the torque exerted about the pivot point? (Use any variable or symbol stated above along with the following as necessary: g and ?.)
(d) Show that ?? = I? with at = L? gives the same tangential acceleration as found in Part (a)

Explanation / Answer

You need to first find the tangential FORCE, because then you can use the equation:

tangential_acceleration = tangential_force / m
(that's just the same equation as "F=ma")

To find the tangential force, look at all the forces acting on the bob, and add up the tangential components of the individual forces.

The only forces are: the tension of the string, and bob's weight.

The tension has NO tangential component, because it pulls in a direction perpendicular to the tangential direction.

The weight has a tangential component equal to: (mg)sin(16

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