Which of the following is/are true of the relationship between rotational and linear motion?

s = r*9

angular velocity, w, is a vector

angular acceleration, a, is a vector.

all options a-c are correct

only options a-b are correct

2. Which of the following are true of vector math?

a) The dot product between a vector and itself gives you 0.

b) The dot product between a vector and an exact same vector in the opposite direction gives you -1 .

c) the cross product of a vector with itself gives you 1.

d) the cross product of a vector with the same vector but in the opposite direction gives you -1 .

3. Which of the following statements are true of tangential and centripetal acceleration?

a) centripetal acceleration can sometimes act in a direction that is away from the center of rotation

b) centripetal acceleration and tangential acceleration are co-dependent on each other

c) the cross product of centripetal and tangential acceleration is 0

d) centripetal and tangential accelerations occur at 90 degrees to each other

1. Which of the following statements are true of moment of inertia?

a) For a given body (e.g., a sphere or a cube), the position of the axis about which the moment of inertia

b) is calculated (i.e., the axis of rotation in our case) will affect its value.

c) the moment of inertia of a uniform thin walled hollow sphere (about an axis passing through its center

d) of mass) is less than that of a uniform solid sphere (about an axis passing through its center of mass)

e) c) a single mass M, spinning at the end of a string a distance R from the axis of rotation, has the same

f) value for moment of inertia as a solid uniform cylinder spinning about a central axis.

g) the moment of inertia of a rotating system will always be greater than its mass

h) only options a-b are correct

2. Which of the following is/are true of angular momentum?

a) torque is time derivative of angular momentum

b) angular momentum is conserved in a system that has no losses (like friction)

c) angular momentum is a vector quantity

d) a-c are all correct

1. The total kinetic energy of a rigid body (of mass M) as seen in an inertial frame is the sum of the kinetic energy of a particle of mass M moving with the velocity of the center of mass and the kinetic energy of motion (or
rotation) of the rigid body about its center of mass.

        True

        False

     2. When a sphere or a cylinder rolls on a flat surface, if there is no friction, the body will experience purely rotational motion.

        True

        False

  3. In the rotational frame, work done between two instances of rotational states is nothing but the difference in rotational kinetic energy between those states

        True

        False

4. The unit for power in rotational kinematics is different from what it is in linear kinematics

        True

        False

5. The presence of a net external torque will still lead to a conservation of angular moment of a rotating body

        True

False

Question

Which of the following is/are true of the relationship between rotational and linear motion?
1. s = r*9
2. angular velocity, w, is a vector
3. angular acceleration, a, is a vector.
4. all options a-c are correct
5. only options a-b are correct

2. Which of the following are true of vector math?

a) The dot product between a vector and itself gives you 0.

b) The dot product between a vector and an exact same vector in the opposite direction gives you -1 .

c) the cross product of a vector with itself gives you 1.

d) the cross product of a vector with the same vector but in the opposite direction gives you -1 .

3. Which of the following statements are true of tangential and centripetal acceleration?

a) centripetal acceleration can sometimes act in a direction that is away from the center of rotation

b) centripetal acceleration and tangential acceleration are co-dependent on each other

c) the cross product of centripetal and tangential acceleration is 0

d) centripetal and tangential accelerations occur at 90 degrees to each other

1. Which of the following statements are true of moment of inertia?

a) For a given body (e.g., a sphere or a cube), the position of the axis about which the moment of inertia

b) is calculated (i.e., the axis of rotation in our case) will affect its value.

c) the moment of inertia of a uniform thin walled hollow sphere (about an axis passing through its center

d) of mass) is less than that of a uniform solid sphere (about an axis passing through its center of mass)

e) c) a single mass M, spinning at the end of a string a distance R from the axis of rotation, has the same

f) value for moment of inertia as a solid uniform cylinder spinning about a central axis.

g) the moment of inertia of a rotating system will always be greater than its mass

h) only options a-b are correct

2. Which of the following is/are true of angular momentum?

a) torque is time derivative of angular momentum

b) angular momentum is conserved in a system that has no losses (like friction)

c) angular momentum is a vector quantity

d) a-c are all correct

1. The total kinetic energy of a rigid body (of mass M) as seen in an inertial frame is the sum of the kinetic energy of a particle of mass M moving with the velocity of the center of mass and the kinetic energy of motion (or
rotation) of the rigid body about its center of mass.

        True

        False

     2. When a sphere or a cylinder rolls on a flat surface, if there is no friction, the body will experience purely rotational motion.

        True

        False

  3. In the rotational frame, work done between two instances of rotational states is nothing but the difference in rotational kinetic energy between those states

        True

        False

4. The unit for power in rotational kinematics is different from what it is in linear kinematics

        True

        False

5. The presence of a net external torque will still lead to a conservation of angular moment of a rotating body

        True

False

Accepted Answer

Linear movement refers to an object moving from one point to another in a straight line.…

Which of the following is/are true of the relationship between rotational and linear motion? s = r*9 angular velocity, w, is a vector angular acceleration, a, is a vector. all options a-c are correct only options a-b are correct