An object of mass 4kg moves around a circle of radius 6m with a constant speed of 12m/s calculate a.angular speed b.force towards the centre

Answer 1

Please make sure the given information is correct,

mass = 4 kg, radius of the circle = 6m, and constant linear speed = 12 m/s

Firstly, let's look at the force (part b)

If I recall correctly, the normal acceleration, a_n = v²/r and F_n = ma_n

Therefore a_n = 12²/6 = 24 m/s² and gives us F_n = (4 kg) (24 m/s²) = 96 N pointing towards the center of the circle. (it points towards the center because this force/acceleration is causing a change in direction and it always is perpendicular to the instantaneous direction of travel) That is why the linear speed is constant.

Now, for the angular speed (part a).

The units of linear speed would be m/s, while the units for angular speed would be rad/s

And a full circle is 2π radians.

Some books use ω for angular speed.

Two ways to solve, one formula and one logic.

From logic, calculate the circumference of the circle, divide by linear speed, and that's the time it takes to go all the way around. Take 2π and divide by that time, and you get ω in rad/s.

In other words, Circumference = 2πr = 12π, then divide by linear speed, and you see it takes π seconds to get all the way around the circle. Since a full circle is 2π radians, 2π/π gives you ω = 2 rad/sec

Or simply say that ω = v/r = 12/6 = 2 rad/sec.

Hope this helps clear some of the concepts up for you.