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MSTC Physics Chapter 8 Sections 3 & 4

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Sample Problem A 15 N force is applied to a cord wrapped around a pulley of mass 4 kg and radius 33 cm. The pulley accelerates uniformly from rest to an angular speed of 30 rad/s in 3 s. If there is a frictional torque of 1.1 Nm at the axle, determine the moment of inertia of the pulley. The pulley rotates about its center.

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Sample Problem A block of mass 3 kg hangs from a string wrapped around a frictionless, disk-shaped pulley of mass 10 kg and radius 75 cm. If the block descends from rest under the influence of gravity, what is the magnitude of its linear acceleration?

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Question Consider a solid disk and a hoop at the top of a ramp. Both the disk and the hoop have the same mass and the same radius. Both are released from rest. Which will reach the bottom of the ramp first? Why?

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**Rotational Kinetic Energy**

Energy an object has due to its rotation KErot = ½ I ω2 The disk and the hoop have both translational and rotational KE

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Sample Problem A solid disk and a hoop are at the top of a ramp of height H. Both the disk and the hoop have mass M and radius R. IF they both start at the top of the ramp from rest, calculate their respective speeds at the bottom.

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Question Several objects roll without slipping down an incline of vertical height H, all starting from rest at the same moment. The objects are a thin hoop, a spherical marble, a solid cylinder, and an empty soup can. They all have the same mass and radius. In addition, a greased box slides down without friction. In what order do they reach the bottom of the incline?

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Sample Problem A bowling ball of mass 7.3 kg and radius 9 cm rolls without slipping down a lane at 3.3 m/s. Calculate its total kinetic energy.

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**Rotational Work Recall W = Fd If a torque is applied W = τθ**

where τ = torque applied θ = angular displacement (angle turned)

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Sample Problem A merry-go-round has a mass of 1640 kg and a radius of 7.5 m. How much net work is required to accelerate it from rest to a rotation rate of 1 revolution per 8 s? Assume it is a solid cylinder.

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Sample Problem An automobile engine develops a torque of 280 Nm at 2800 rpm. What is the power in watts and in horsepower?

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Sample Problem A person opens a door by applying a 15 N force perpendicular to it at a distance 0.9 m from the hinges. The door is pushed wide open (to 120 degrees) in 2 s. A) How much work was done? B) What was the average power delivered?

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Sample Problem A 2.5 kg pulley of radius 0.15 m is pivoted about an axis through its center. What constant torque is required for the pulley to reach an angular speed of 25 rad/s after rotating 3 revolutions, starting from rest?

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Sample Problem A hoop starts from rest at a height 1.2 m above the base of an inclined plane and rolls down under the influence of gravity. What is the linear speed of the hoop’s center of mass just as the hoop leaves the incline and rolls onto a horizontal surface? (Neglect friction.)

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Comparing rotational and linear motion

Comparing rotational and linear motion

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