Tag: equation of motion of rotating body

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Questions Related to equation of motion of rotating body

Multiple choice physics rotational motion of a rigid body and moment of inertia constant angular acceleration equation of motion of rotating body dynamics of rotational motion about a fixed axis

A uniform rigid rod has length $L$ and mass $m$. It lies on a horizontal smooth surface, and is rotated at a uniform angular velocity $\omega$ about a vertical axle passing through one of its ends. The force exerted by the axle on the rod will be

  1. $m \omega^2 L$ outward

  2. $m \omega^2 L$ inward

  3. $\dfrac{1}{2} m\omega^2 L$ outward

  4. $\dfrac{1}{2} m\omega^2 L$ inward
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice physics rotational motion of a rigid body and moment of inertia constant angular acceleration equation of motion of rotating body dynamics of rotational motion about a fixed axis

A disc and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

  1. Both reach at the same time

  2. Depends on their masses

  3. Disc

  4. Sphere
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Acceleration a = g*sin(theta) / (1 + I/MR^2). The sphere has I = (2/5)MR^2, so a = g*sin(theta) / 1.4. The disc has I = (1/2)MR^2, so a = g*sin(theta) / 1.5. The sphere has higher acceleration and arrives first.

Multiple choice physics rotational motion of a rigid body and moment of inertia constant angular acceleration equation of motion of rotating body dynamics of rotational motion about a fixed axis

A body is given translational velocity and kept on a surface that has sufficient friction. Then:

  1. Body will move forward before pure rolling

  2. Body will move backward before pure rolling

  3. Body will start pure rolling immediately

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

since the body is given initial translational velocity so it will move forward while coming in pure rolling condition.

so the answer is A.

Multiple choice physics rotational motion of a rigid body and moment of inertia constant angular acceleration equation of motion of rotating body dynamics of rotational motion about a fixed axis

(a) A child stands at the center of a turntable with his two arms outstretched. The turntable is set rotating with an angular speed of $40$ rev/min. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to $2/5$ times the initial value? Assume that the turntable rotates without friction. (b) Show that the child’s new kinetic energy of rotation is more than the initial kinetic energy of rotation. How do you account for this increase in kinetic energy?

  1. $300\ rev/min\ and 2.5 E _1$

  2. <span>$100\ rev/min\ and 2.5 E _1$</span>

  3. <span>$500\ rev/min\ and 7.5 E _1$</span>

  4. none of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

By conservation of angular momentum, I1*omega1 = I2*omega2. Given I2 = (2/5)I1, then omega2 = (5/2)omega1 = 2.5 * 40 = 100 rev/min. KE2 = (1/2)I2*omega2^2 = (1/2)(2/5)I1(2.5*omega1)^2 = 2.5 * KE1.