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23 Nov 2019

A block (mass = 1.3 kg) is hanging from a massless cord that is wrapped around a pulley (moment of inertia = 1.7 x 10-3 kg·m2), as the figure shows. Initially the pulley is prevented from rotating and the block is stationary. Then, the pulley is allowed to rotate as the block falls. The cord does not slip relative to the pulley as the block falls. Assume that the radius of the cord around the pulley remains constant at a value of 0.032 m during the block's descent. Find (a) the angular acceleration of the pulley and (b) the tension in the cord. see textbook for picture.

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

a) At the bottom is a 3 step pulley; consisting ofthree wheelsof different diameters.b) The rotating arm has two massesattached,and is screwed into the 3 step pulley. Whenthe pulleyrotates, so does the rod.c) The string is wrapped around one ofthewheels in the 3 step pulley and passes overthe smart pulley. Themass hanger is hooked into the loop at the end of the string.d)When the system is released, the mass hanger falls, turning thesmart pulley, and the 3 step pulley withthe rod attached. e)Assume: that the smart pulley is very light, so its moment ofinertia is negligible as compared to the moment of inertia of the 3step pulley and rod.



Suppose that you measured the moment of inertia of the system as I= 5.05 kg-m2. Assume the diameter of the pulley around which youwrap the string is d = 2.5 cm.

a) Suppose the system is initially spinning at angular speed ωo =9.27 rad/s. After you drop a disk of mass 856 g on it, the systemrotates at ωf = 8.35 rad/s. Find:
- the moment of inertia of the disk: kg-m2
- the radius of the disk: cm

b) suppose the system is initially spinning at angular speed ωo =2.05 rad/s. After you drop a cube of mass 786 g on it, the systemrotates at ωf = 1.79 rad/s. Find:
- the moment of inertia of the cube: kg-m2
- the length of one side of the cube: cm

a) At the bottom is a 3 step pulley; consisting ofthree wheelsof different diameters.b) The rotating arm has two massesattached,and is screwed into the 3 step pulley. Whenthe pulleyrotates, so does the rod.c) The string is wrapped around one ofthewheels in the 3 step pulley and passes overthe smart pulley. Themass hanger is hooked into the loop at the end of the string.d)When the system is released, the mass hanger falls, turning thesmart pulley, and the 3 step pulley withthe rod attached. e)Assume: that the smart pulley is very light, so its moment ofinertia is negligible as compared to the moment of inertia of the 3step pulley and rod.

a)when you drop the mass holder, the system rotates at angularacceleration α. If you wrapped thestring around a larger diameter pulley and dropped the mass holder,the acceleration of the system would be:

exactlyα? less than a? more than a?
Suppose that you measured themoment of inertia of the system as I = 5.05 kg-m2. Assume the diameterof the pulley around which you wrap the string is d =2.5 cm.

a) In trial 1:the system is initially spinning at angular speedωo = 9.27 rad/s. After you drop a disk of mass856 g on it, the system rotatesat ωf = 8.35 rad/s. Find:
- the moment of inertia of thedisk: kg-m2
- the radius of the disk: cm

b) In trial 3: suppose the system is initially spinning at angularspeed ωo = 2.05 rad/s. After you drop a cube of mass786 g on it, the system rotatesat ωf = 1.79 rad/s. Find:
- the moment of inertia of thecube: kg-m2
- the length of one side of the cube: cm

Refer to picture on bottom.

a) At the bottom is a 3 step pulley; consisting ofthree wheelsof different diameters.b) The rotating arm has two massesattached,and is screwed into the 3 step pulley. Whenthe pulleyrotates, so does the rod.c) The string is wrapped around one ofthewheels in the 3 step pulley and passes overthe smart pulley. Themass hanger ishooked into the loop at the end of the string.d) Whenthe system is released, the mass hanger falls, turning the smartpulley, and the 3 step pulley withthe rod attached.e) Assume: thatthe smart pulley is very light, so its moment of inertia isnegligible as compared to themoment of inertia of the 3 step pulleyand rod.

Suppose the rod has mass M = 867 g, length L = 49.3 cm, and rotates on a fixed,frictionless axis through the center of mass. Initially, assumethere are no masses attached to the rod.

a) Find the moment of inertia of the rod.
kg-m2

b) Now, assume two point masses of massm = 681 g are attachedto the rod, one on each side, at distance r = 22.3 cm from the center of mass of the rod.Find the moment of inertia of the rod-plus-masses system.
kg-m2

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