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B.Tech Robotics Rotational Motion and Angular Momentum — practice questions — page 2

Explore 56 free Rotational Motion and Angular Momentum questions in B.Tech Robotics Mechanics. Open each question or exercise to read its content, reference answers and available explanation.

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Rotational Motion and Angular Momentum questions and exercises with answers

Showing questions 31–56 of 56.

A force perpendicular to r acts on a point mass m at distance r from a pivot. Which relation follows from Newton's second law?Read the answer and worked solution →How is the moment of inertia of an extended body built up, and what does it depend on?Read the answer and worked solution →What is the moment of inertia of a hoop about its own central axis?Read the answer and worked solution →What is the rotational analogue of Newton's second law?Read the answer and worked solution →In SI units, what are the units of moment of inertia?Read the answer and worked solution →A merry-go-round is a uniform disk of mass 50.0 kg and radius 1.50 m. What is its moment of inertia about the central vertical axis?Read the answer and worked solution →What is the work done by a net torque that turns a body through an angle theta?Read the answer and worked solution →What is the rotational kinetic energy of a body with moment of inertia I turning at angular velocity omega?Read the answer and worked solution →What does the net work done by a torque on a rotating body equal?Read the answer and worked solution →A grindstone starting from rest is given an angular acceleration of 14.7 rad/s^2 and turns through 1.00 rad. What is its final angular velocity?Read the answer and worked solution →A helicopter rotor of moment of inertia 1067 kg m^2 turns at 300 rpm. What is its rotational kinetic energy?Read the answer and worked solution →If all of the 5.26 x 10^5 J of rotational energy in a helicopter rotor could be used to lift the 1000 kg machine, how high would it rise?Read the answer and worked solution →A solid cylinder of mass 0.750 kg and radius 4.00 cm rolls from rest without slipping down an incline 2.00 m high. What is its speed at the bottom?Read the answer and worked solution →What practical use is made of the large rotational kinetic energy that a heavy spinning disk can hold?Read the answer and worked solution →Why must a helicopter pilot never let the rotor slow below a critical angular velocity in flight?Read the answer and worked solution →How is angular momentum defined, and what are its SI units?Read the answer and worked solution →How does net torque relate to angular momentum?Read the answer and worked solution →Under what condition is the angular momentum of a system conserved?Read the answer and worked solution →A skater has 2.34 kg m^2 at 0.800 rev/s with arms out, and 0.363 kg m^2 at 5.16 rev/s with arms in. What are her rotational kinetic energies before and after?Read the answer and worked solution →Earth is treated as a uniform sphere of mass 5.979 x 10^24 kg and radius 6.376 x 10^6 m, turning once per day. What is its angular momentum?Read the answer and worked solution →What keeps Earth turning, and what is slowly changing its rate of spin?Read the answer and worked solution →About how long was a day on Earth some 900 million years ago?Read the answer and worked solution →A hinged stick is struck at various points along its length. At which point is no force delivered to the hinge?Read the answer and worked solution →How is the direction of angular velocity and angular momentum found for a spinning disk?Read the answer and worked solution →A torque acts on a spinning body. In which direction does its angular momentum change?Read the answer and worked solution →Angular momentum is a vector. Is rotational kinetic energy also a vector?Read the answer and worked solution →

Worked practice questions

A force perpendicular to r acts on a point mass m at distance r from a pivot. Which relation follows from Newton's second law?

  1. tau = m r alpha
  2. tau = m alpha / r
  3. tau = m r^2 alpha
  4. tau = m r^2 alpha^2
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Correct answer: C. tau = m r^2 alpha

1. Newton's second law for the point mass gives F = m a. 2. For circular motion a = r alpha, so F = m r alpha. 3. Because F is perpendicular to r, the torque is simply tau = r F. 4. Multiplying both sides by r gives r F = m r^2 alpha, that is tau = m r^2 alpha. 5. The quantity m r squared plays the role of mass and is the moment of inertia of the point mass. 6. Squaring alpha would break the direct proportionality between torque and angular acceleration. _Source: OpenStax College Physics (CC BY 4.0), Ch 10 "Rotational Motion and Angular Momentum", section 10.3 Dynamics of Rotational Motion: Rotational Inertia_

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How is the moment of inertia of an extended body built up, and what does it depend on?

  1. Product of m and r, and on the body speed
  2. Sum of m r squared, and on nothing else
  3. Sum of m times r, and on the chosen axis
  4. Sum of m r squared, and on the chosen axis
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Correct answer: D. Sum of m r squared, and on the chosen axis

1. Any object can be treated as a collection of point masses. 2. Each point mass contributes m r squared, so the total is I = sum of m r squared. 3. Every r is measured from the axis, so the answer changes if the axis changes. 4. A moment of inertia quoted without naming its axis is therefore incomplete. _Source: OpenStax College Physics (CC BY 4.0), Ch 10 "Rotational Motion and Angular Momentum", section 10.3 Dynamics of Rotational Motion: Rotational Inertia_

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What is the moment of inertia of a hoop about its own central axis?

  1. M R squared divided by two
  2. M R squared divided by three
  3. Two M R squared over five
  4. M R squared, with no fraction
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Correct answer: D. M R squared, with no fraction

1. Moment of inertia is the sum of m r squared over all the mass of the body. 2. A hoop has all of its mass at the same distance R from the axis. 3. The sum then factors to M R squared with no fraction in front. 4. Half M R squared belongs to a solid disk, where much of the mass sits nearer the axis. _Source: OpenStax College Physics (CC BY 4.0), Ch 10 "Rotational Motion and Angular Momentum", section 10.3 Dynamics of Rotational Motion: Rotational Inertia_

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