A uniform prismatic rod of length / and mass m is placed in a vertical position with one end on a smooth horizontal floor. It is then let go, and it falls to the floor from rest in the vertical position. Assuming that the rod never loses contact with the floor, derive an expression for its angular velocity at any position as shown in Figure 7(a). =0 Figure 7(a) Determine the height hat which the billiard ball of radius r must be struck so that no frictional force develops between the ball and the table at A as shown in Figure 7(b). Assume that the cue only exerts a horizontal force P on the ball. Take IG of the ball equal to (2/5)mr, where m is the mass of the ball.
A uniform prismatic rod of length / and mass m is placed in a vertical position with one end on a smooth horizontal floor. It is then let go, and it falls to the floor from rest in the vertical position. Assuming that the rod never loses contact with the floor, derive an expression for its angular velocity at any position as shown in Figure 7(a). =0 Figure 7(a) Determine the height hat which the billiard ball of radius r must be struck so that no frictional force develops between the ball and the table at A as shown in Figure 7(b). Assume that the cue only exerts a horizontal force P on the ball. Take IG of the ball equal to (2/5)mr, where m is the mass of the ball.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Step 1: Write the given data and what is to find
VIEWStep 2: (a) Draw the free body diagram:
VIEWStep 3: Write the expression for the kinetic and rotational energy of a differential element on the rod:
VIEWStep 4: Derive the expression for the angular velocity of the rod:
VIEWStep 5: (b) Determine the height h:
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