**Q.1) A uniform rod of length L and mass M is pivoted at its midpoint. It is initially at rest and then released. What will be the angular acceleration of the rod just after it is released?**

**A) 2g/L**

- B) 3g/L

- C) 4g/L

- D) 5g/L

**Answer:**

**The correct answer is A) 2g/L.**

#### Explanation:

When the rod is released, gravity exerts a torque on it, causing it to rotate about the pivot point. The torque is given by T = IÎ±, where I is the moment of inertia of the rod and Î± is the angular acceleration. Since the rod is rotating about its midpoint, the moment of inertia is (1/12)ML^2.

The torque due to gravity is Mg/2, where g is the acceleration due to gravity. Therefore, we have:

Mg/2 = (1/12)ML^2 * Î±

Simplifying this equation, we get:

Î± = 2g/L

Therefore, the angular acceleration of the rod just after it is released is 2g/L, which is option A.

**Q2.)**

**A uniform thin rod of length L and mass M is rotated about its midpoint with an angular speed of Ï‰. If it is now rotated about one of its ends, the angular speed will be:**

**A) Ï‰**

- B) 2Ï‰

- C) 3Ï‰/2

- D) 4Ï‰/3

#### Explanation:

**Q3.)**

**A rotation is a transformation that:**

- a) changes the size of a figure

- b) changes the shape of a figure

**c) moves a figure around a fixed point**

- d) reflects a figure across a line

**Answer: c)**moves a figure around a fixed point

**Q4.)**

**The fixed point of a rotation is called the:**

**a) center**

- b) vertex

- c) origin

- d) focus

**Answer: a) center**

**Q5.)**

**A rotation of 90 degrees clockwise is the same as a rotation of ____ degrees counterclockwise.**

- a) 90

- b) 180

**c) 270**

- d) 360

**Answer: c)**270

**Q6.)**

**Which of the following is a true statement about rotations?**

- a) A rotation can be performed in any direction.

- b) A rotation always changes the orientation of a figure.

**c) A rotation preserves the length of a figure's sides.**

- d) A rotation changes the position of a figure's vertices.

**Answer: c)**A rotation preserves the length of a figure's sides.

**Q7.)**

**The image of a figure after a rotation can be found by:**

- a) adding the coordinates of the original figure to the coordinates of the center of rotation

- b) subtracting the coordinates of the original figure from the coordinates of the center of rotation

**c) multiplying the coordinates of the original figure by a rotation matrix**

- d) dividing the coordinates of the original figure by the angle of rotation

**Answer: c)**multiplying the coordinates of the original figure by a rotation matrix.

**Q8.) What is rotation in geometry?**

- a) Movement of a point along a line

**b) Movement of a point around a fixed point**

- c) Movement of a point in a straight line

- d) Movement of a point in a circular path

**Answer: b)**Movement of a point around a fixed point

**Q9.) What is the center of rotation?**

**a) The point around which the object is rotated**

- b) The point on the object that remains fixed during rotation

- c) The point on the object that moves during rotation

- d) The point from where the rotation starts

**Answer: a)**The point around which the object is rotated

**Q10.)**

**What is the angle of rotation?**

**c) The angle through which the object is rotated**

**Answer: c)**The angle through which the object is rotated

**Q11.)**

**In a clockwise rotation, what is the direction of rotation?**

- a) Counter-clockwise

- b) From top to bottom

- c) From right to left

**d) From left to right**

**Answer: d)**From left to right

**Q12.)**

**If an object is rotated 90 degrees clockwise, what will be its image?**

- a) A reflection of the object

- b) An object with its sides interchanged

- c) An object rotated 90 degrees anti-clockwise

**d) An object rotated 90 degrees clockwise**

**Answer: d)**An object rotated 90 degrees clockwise

**Q13.)**

**Which of the following is a unit of measurement for rotational speed?**

- a) Watts

- b) Joules

- c) Radians

- d) RPM (Revolutions per minute)

**ANS: d) RPM (Revolutions per minute)**

**Q14.)**

**A point that does not move during rotation is called the:**

- a) Center of mass

**b) Axis of rotation**

- c) Angular momentum

- d) None of the above

**ANS: b) Axis of rotation**

**Q15.)**

**What is the direction of the angular velocity vector for counterclockwise rotation?**

- a) Up

- b) Down

**c) Left**

- d) Right

**ANS: c) Left**

**Q16.)**

**A rigid object is rotating with a constant angular velocity. Which of the following statements is true?**

- a) The object is not experiencing any torque

- b) The object is accelerating

- c) The object is losing kinetic energy

- d) None of the above

**ANS: a)**The object is not experiencing any torque

**Q17.)**

**Which of the following is an example of rotational motion?**

- a) A car moving along a straight road

**b) A rollercoaster going up and down hills**

- c) A basketball being dribbled on a court

- d) None of the above

**ANS: b)**A rollercoaster going up and down hills