PART A A uniform meter stick of 0.5kg in mass is pivoted at the 25cm mark as shown in the diagram. pivot 30° 25cm 0.2kg 0.3kg (a) What is the magnitude of the total torque about the pivot point (do not forget the torque due to the weight of the meter stick). What is the direction of the total torque as a vector? (b) What is the moment of inertia of the meter stick about the pivot? What is the angular acceleration?

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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PART A
A uniform meter stick of 0.5kg in mass is pivoted at the 25cm mark as shown in the diagram.
pivot
30°
E 25cm
0.2kg
0.3kg
(a) What is the magnitude of the total torque about the pivot point (do not forget the torque
due to the weight of the meter stick). What is the direction of the total torque as a vector?
(b) What is the moment of inertia of the meter stick about the pivot? What is the angular
acceleration?
Transcribed Image Text:PART A A uniform meter stick of 0.5kg in mass is pivoted at the 25cm mark as shown in the diagram. pivot 30° E 25cm 0.2kg 0.3kg (a) What is the magnitude of the total torque about the pivot point (do not forget the torque due to the weight of the meter stick). What is the direction of the total torque as a vector? (b) What is the moment of inertia of the meter stick about the pivot? What is the angular acceleration?
PART B
Rolling without slipping
M
y
a
X4
(a) What is the moment of inertia of the sphere in terms of M and R?
(b) Draw all the forces acting on the solid sphere in the above figure.
(c) Using Newton's Second Law, write down the equation of motion for the center of the sphere
along the x-direction defined in the figure.
(d) Using Newton's Second Law for rotational motion, write down the equation of rotational
motion.
(e) Solve for the acceleration a from the two equations you obtained in parts (c) and (d).
Assume the sphere is rolling without slipping, so do not forget there is a relationship between a
and a.
Transcribed Image Text:PART B Rolling without slipping M y a X4 (a) What is the moment of inertia of the sphere in terms of M and R? (b) Draw all the forces acting on the solid sphere in the above figure. (c) Using Newton's Second Law, write down the equation of motion for the center of the sphere along the x-direction defined in the figure. (d) Using Newton's Second Law for rotational motion, write down the equation of rotational motion. (e) Solve for the acceleration a from the two equations you obtained in parts (c) and (d). Assume the sphere is rolling without slipping, so do not forget there is a relationship between a and a.
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