Q.79

Expert-verifiedFound in: Page 334

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

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

L_{i}= L_{f }..............................................(1)

Get initial momentum

L_{i}= I_{i }ω_{i.}............................................(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

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