A 200 g, 40-cm-diameter turntable rotates on frictionless bearings at 60 rpm. A 20 g block sits at the center of the turntable. A compressed spring shoots the block radially outward along a frictionless groove in the surface of the turntable. What is the turntable’s rotation angular velocity when the block reaches the outer edge?
The turntable’s angular velocity is 5.76 rad / sec
mass of turn table = 200 gm = 0.2 kg
Diameter of turntable = 40 cm = 0.4 m
so radius of turn table =0.2 m
mass of block = 20 gm =0.02 kg
rpm = 60.
covert rpm into rad/sec = 2π rad/sec
Use the law of conservation for momentum
initial momentum = final momentum
Li= Lf ..............................................(1)
Get initial momentum
Li= Ii ωi.............................................(2)
Find moment of inertia
Substitute this in equation(2)
Substitute the given value
Now find the final momentum
Substitute the given values
Equate (4) and (6) we get
A satellite follows the elliptical orbit shown in FIGURE P12.77. The only force on the satellite is the gravitational attraction of the planet. The satellite’s speed at point a is 8000 m/s.
a. Does the satellite experience any torque about the center of the planet? Explain. b. What is the satellite’s speed at point b? c. What is the satellite’s speed at point c?
Luc, who is 1.80 m tall and weighs 950 N, is standing at the center of a playground merry-go-round with his arms extended, holding a 4.0 kg dumbbell in each hand. The merry-go-round can be modeled as a 4.0-m-diameter disk with a weight of 1500 N. Luc’s body can be modeled as a uniform 40-cm-diameter cylinder with massless arms extending to hands that are 85 cm from his center. The merry-go-round is coasting at a steady 35 rpm when Luc brings his hands in to his chest. Afterward, what is the angular velocity, in rpm, of the merry-go-round?
The sphere of mass M and radius R in FIGURE P12.76 is rigidly attached to a thin rod of radius r that passes through the sphere at distance 12 R from the center. A string wrapped around the rod pulls with tension T. Find an expression for the sphere’s angular acceleration. The rod’s moment of inertia is negligible.
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