Question

a body of mass 50 into 10 to the power minus 3 kg is moving in a circle of diameter 1 m at an angular speed 360 r.p.m calculate it's centripetal acceleration and the centripetal force acting on it
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Answer 1

Solution :

As per the given data ,

• Mass of the body (m)= 50 x 10 ^-3 = 0.05 kg
• Diameter of the circle(d) = 1 m
• Radius of the circle(r) = d / 2 = 1 / 2 = 0.5 m
• Frequency(f) = 360 rpm

We need to convert rpm into rps in order to do that simply divide by 60

Frequency = 360 / 60 = 60 rps

We know that ,

→ ω = 2 π f

→ ω = 2 x 3.14 x 60

→ ω = 376.8 rad / s

The linear velocity of the mass is given by ,

→ v = ω r

→ v = 376.8 x 0.5

→ v = 188.4 m/s

The centripetal acceleration acting on the mass is given by ,

→ a = v ² / r

→ a = 188.4 x 188.4 / 0.5

→ a = 70989 m/s²

The centripetal acceleration acting on the body is 70989 m/s²

Now let us find the centripetal force acting on the mass  ,

By applying Newton's second law ,

→ F = ma

→ F = 0.05 x 70989

→ F = 3549 N

The centripetal force acting on the body  is 3549 N .