AQA A-level Physics Circular motion
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A body moving around in a circle at a constant speed is accelerating, since its direction and thus its velocity are changing. According to Newton's Second Law, a force must be acting on the body. For the speed to be constant, the force must be perpendicular to the speed and direction of modion, which is tangential to the path. Therefore, there is a resultant force called the centripetal force acting towards the centre of the circle, along its radius. The angular displacement is the angle covered by the body, θ = arc/radius, and is given in radians. Angular speed is the rate of change of angular displacement, ω = θ/t, and is given in rad/s.
By Newton's Second Law, since there is a resultant force acting towards the centre of the circle a body is travelling in, there must be an acceleration acting in the direction of the centripetal force. This is called the centripetal acceleration and its units are m/s². Centripetal acceleration can be calculated using the following: a = vω = rω² = v²/r. Using F = ma, it can now be deduced that centripetal force can be calculated using the following: F = mvω = mrω² = mv²/r.
A horse runs over a circular bridge. Give an expression for the centripetal force acting on the horse for when it is at the top of the bridge, ie. the normal contact force and weight are in line with each other.
A bead of mass 200 g is suspended from a rope in tension. The bead is made to move in a horizontal circle of radius 70 cm. Given that the constant speed of the bead is 9 m/s and that the angle the rope makes with the vertical is 25˚, calculate the tension in the rope.
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