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A mass-less string is wrapped several times around a Cylinder . If the free end…

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Wize University Physics Textbook (Master) > Angular / Rotational Motion

Moment of Inertia

5 Activities

Wize University Physics Textbook (Master) > Angular / Rotational Motion

Torque

3 Activities

A mass-less string is wrapped several times around a Cylinder . If the free end of the string is held in place and the Cylinder is released form rest, the string unwinds and the Cylinder descends. What is the acceleration of the Cylinder ?


More Moment of Inertia Questions:
A horizontal platform in a shape of a disk rotates on a frictionless bearing about a vertical axle through the center of the disk. The platform has a mass of 200 kg and radius of 3.0 meters. A student with mass 80 kg, walks from the edge towards the center of the platform.
a) Find the moment of inertia of the disk.
b) If the angular speed of the disk is 2 rad/s, when the student moves another meter towards the center, find their angular speed.
Moment of inertia is same as linear inertia
Instead of mass (used in translational motion), what do we use in the equation for rotational kinetic energy instead?
A thin uniform rod (length=1m, mass = 5kg) is pivoted about a horizontal, frictionless pin through one end of the rod. The rod is released when it makes an angle of 60°60\degree above the horizontal. What is the angular acceleration of the rod at the instant it is released? (pick the closest answer)
Two thin Hoops each of mass M and radius of R are joined together as shown in the figure. What is the moment of inertia for rotations in the plane of the page about pint O?
A 10 kg mass is hanging from a rope wrapped around a pulley. The falling mass causes the pulley to rotate. The mass of the pulley is 2 kg. What is the acceleration of the falling mass, and what is the tension of the rope?
Robin Hood and Marian decide to build a snowmen at the edge of a cliff.  The snowman consists of three spheres with radii 90 cm, 60 cm and 30 cm, and the density of snow is 300kg/m3300kg/m^3.  Little John is a jerk and pushes the snowman over the cliff.  The snowman begins to rotate around its center of mass as it falls.  What is the moment of inertia of the snowman as it’s falling? (For a solid sphere, ICM=25MR2 , and  V=43πR3I_{CM}=\frac{2}{5}MR^2\ ,\ and\ \ V=\frac{4}{3}\pi R^3, )
A potter's wheel of mass 7.00 kg and radius 0.650 m spins about its central axis. A 2.10 kg lump of clay is dropped onto the wheel at a distance 0.410 m from the axis. Calculate the final rotational inertia of the system.
Rotational inertia depends on the force of gravity
moment of interia
What does the moment of inertia describe?
The moment of inertia of a body depends on
More Torque Questions:
Torque on a Circular Current Loop
Practice: Torque on a Circular Current Loop
A circular loop of radius 10.5 cm and 40 turns has a current of 2.50 A flowing through the coil. A magnetic field of strength 3.4 T acts at an angle of 35º to the normal of the plane of the loop. What is the magnitude of the net torque acting on the loop?
Practice: Torque on a Circular Current Loop
A circular loop of radius 10.5 cm and 40 turns has a current of 2.50 A flowing through the coil. A magnetic field of strength 3.4 T acts at an angle of 35º to the normal of the plane of the loop. What is the magnitude of the net torque acting on the loop?
One end of a uniform 4.0 m-long rod of weight w{\small w} is supported by a cable at an triangle of θ = 37°{\small \theta\ =\ 37\degree}with the rod. The other end rests against a wall, where it is held by friction, as shown. The coefficient of static friction between the wall end the rod is μs = 0.50.{\small \mu_s\ =\ 0.50.} Determine the minimum distance x{\small x} from point A at which an additional weight w{\small w} (the same as the weight of the rod) can be hung without causing the rod to slip at point A. Enter your answer in meters to the appropriate number of sig figs.
Forces: Standing on a beam
A horizontal beam with a length of 8.0 meters and weight of 200 N is attached to a wall by a pin connection. Its far end is attached to the cable that makes angle of 53 degrees with the beam. A person of weight 600 N stands 2.0 meters away from the wall. What is the tension of the cable (T) and the magnitude of the force that wall applies on the beam (R), respectively?
Hint: The total reaction force is the sum of a normal force (perpendicular to the wall) and a friction force (parallel to the wall). So the net reaction force will be at an angle. (In this problem we are not ignoring friction at the wall). In this problem, there are a few ways to solve it; but you can just treat the reaction force as a single force that provides a single torque at an angle to find the answer.
Practice: Balanced beam
A uniform 90 kg beam is resting on two supports as shown below. The supports are 20 cm and 80 cm away from the two ends of beam. If the beam is 180 cm, what are the forces acting on the beam from supports A and B?
A 3.0 m ladder of mass 12 kg rests against a frictionless wall. The coefficient of friction between the ladder and the floor is 0.60. Assume there is no friction between the wall and the ladder. What is the smallest angle that the ladder can make with the ground if the ladder is to remain at rest? (Enter your answer in degrees)
Forces: Torque
A seesaw of length 5m is supported at the center. A child of mass 35kg is sitting on one end. A second child of mass 45kg comes to play. Where should the second child sit in order to balance the seesaw? Enter your answer in meters, measured from the pivot axis of the seesaw.
Find the net torque on the wheel below about the axle through Operpendicular to the page, taking a = 10.0 cm and b = 25.0 cm. (Note for clarification: the 12.0 N force is acting directly above the axis O, at an angle from that point.) Give your answer in units of Nm to the appropriate number of significant figures.
Calculate the net torque (magnitude and direction) on the beam through the point labelled O (i.e. an axis perpendicular to the page at point O) and (b) through an axis through C perpendicular to the page. Give your answers in Nm.
A thin uniform rod (length=1m, mass = 5kg) is pivoted about a horizontal, frictionless pin through one end of the rod. The rod is released when it makes an angle of 60°60\degree above the horizontal. What is the angular acceleration of the rod at the instant it is released? (pick the closest answer)
A 10 kg mass is hanging from a rope wrapped around a pulley. The falling mass causes the pulley to rotate. The mass of the pulley is 2 kg. What is the acceleration of the falling mass, and what is the tension of the rope?
Practice: Condition of Static Equilibrium
A 3.0 m ladder of mass 12 kg rests against a frictionless wall. The coefficient of friction between the ladder and the floor is 0.60. What is the smallest angle that the ladder can make with the ground if the ladder is to remain at rest? (in degrees) Neglect the friction between the ladder and the wall.
Is the force exerted by the tendon attached to the forearm to hold the forearm horizontal greater than, equal to, or less than the weight of the forearm?
If a man can push with a maximum force of 90 N, how far from the door's rotation axis must he apply this force if 110-Nm torque is needed to start rotating a revolving door?
A wooden beam of mass 150 kg and length 10m is suspended from a horizontal wall support at the left end and connected by a cable to the same wall at the right end. The cable makes an angle of 45º with the horizontal. A person of mass 42 kg stands on the beam 2.5 m from the left wall. A 25 kg child also rests on the beam, at 7m from the left wall. Calculate the tension in the rope and the force exerted by the wall on the beam.
Newton’s First Law does not apply to rotating objects
torque
Calculate the net torque (magnitude and direction) on the beam through the point labelled O (i.e. an axis perpendicular to the page at point O) and (b) through an axis through C perpendicular to the page. Give your answers in Nm.
Torque due to a Magnetic Field
A circular loop of radius 10.5 cm and 40 turns has a current of 2.50 A flowing through the coil. A magnetic field of strength 3.4 T acts at an angle of 35º to the normal of the plane of the loop. What is the magnitude of the net torque acting on the loop?