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

(a)   The pendulum and the forces acting on it are shown.The tangential force is mgsin q. Therefore, the tangential acceleration is at = gsin q.

(b)   The tension causes no torque. The torque due to the weight about the pivot is mgLsin q.

(b)   Here I = mL2; so a = mgLsin q/mL2 = g sin q/L, and at = g sin q.

(a)   The pendulum and the forces acting on it are shown.The tangential force is mgsin q. Therefore, the tangential acceleration is at = gsin q.

(b)   The tension causes no torque. The torque due to the weight about the pivot is mgLsin q.

(b)   Here I = mL2; so a = mgLsin q/mL2 = g sin q/L, and at = g sin q.

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