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Question

A particle A moves along a circle of radius R=10 cm so that its radius vector r relative to O rotates with constant angular velocity ω=0.2 rad/s. Find the magnitude of the velocity of the particle and its total acceleration.


A
4 cm/s, 1.6 cm/s2
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B
4 cm/s, 2.6 cm/s2
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C
12 cm/s, 1.6 cm/s2
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D
12 cm/s, 1.8 cm/s2
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Solution

The correct option is A 4 cm/s, 1.6 cm/s2

Given that ω0=0.2 rad/s,R=10 cm=0.1 m
θc=2θo (from property of circle)
ωc=2ωo=0.4rad/s
(i) Magnitude of velocity |v|=ωc×R=(0.4)(0.1)
|v|=0.04 m/s or 4 cm/s
(ii) Magnitude of total acceleration |a|=ω2c×R (for uniform circular motion)
|a|=(0.4)2(0.1)=0.016m/s2
|a|=1.6cm/s2

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