Question

Asked Jun 3, 2019

A 2.60-kg hoop 1.80 m in diameter is rolling to the right without slipping on a horizontal floor at a steady 2.70 rad/s .

- Find the magnitude of the velocity vector of each of the following points, as viewed by a person at rest on the ground: (i) the highest point on the hoop; (ii) the lowest point on the hoop, (iii) a point on the right side of the hoop, midway between the top and the bottom.
- Find the magnitude of the velocity vector for each of the points in part C, except as viewed by someone moving along with same velocity as the hoop.

Step 1

Case 1 : Viewed by person at rest.

Since the loop is rolling without slipping the velocity vector can be calculated using angular velocity.

(i)At highest point on the loop:

Write the expression for the velocity at centre of mass of the hoop.

Step 2

The velocity at the highest point is twice the velocity at the canter of mass.

Write the expression for the velocity at highest point of the hoop, and substitute the corresponding terms.

Step 3

(ii) At the lowest point of the hoop.

The velocity of the hoop at the lowest poi...

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