When a body is whirled in a vertical circle at the end of the string tension in the string is maximum:
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Tension is greatest at the lowest point in a vertical circle.
When a body moves along a circular path, its velocity:
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Velocity includes direction, which continuously changes in circular motion.
Angular acceleration is produced by:
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Torque produces angular acceleration.
The rate of change of angular momentum of a body is:
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Torque equals the rate of change of angular momentum.
The necessary centripetal force to the moving car around a corner track is provided by:
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For a car turning on an ordinary road, static friction supplies centripetal force.
An orbiting satellite around the earth receives centripetal force from:
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Earth's gravitational attraction provides the centripetal force.
A car of mass 1000 kg moves on a circular road with a speed of 20 m/s. Its direction changes by 90° after travelling 628 m on the road. The centripetal force acting on the car is:
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For a quarter circle, s = πr/2; then use F = mv²/r.
The moments of inertia of two spheres of equal masses about their respective diameters are same. One of them is solid and the other is hollow. The ratio of the diameter of the solid sphere to that of the hollow sphere is:
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Use Isolid = 2MR²/5 and Ihollow = 2MR²/3, then equate them.
What remains constant in the field of central force:
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A central force produces no torque about the center, so angular momentum is conserved.
As we go below the surface of the earth, the value of g:
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Inside a uniform Earth, g decreases with depth and becomes zero at the center.
The moment of linear momentum is called:
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Angular momentum is the moment of linear momentum.
If R is the radius of the earth and g is the acceleration due to gravity on the surface of the earth, the mean density of the earth is:
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Use g = GM/R² and M = 4πR³ρ/3.
Angular momentum of a body under a central force is:
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A central force has zero torque about the center, so angular momentum is conserved.
A point on the rim of wheel moves 0.2 m when the wheel turns through an angle of 0.25 rad. The radius of wheel is:
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Arc length s = rθ, so r = 0.2/0.25.
Einstein's theory states that bodies and light rays move along:
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In general relativity, free bodies and light follow geodesics in spacetime.
The moment of inertia of a solid cylinder about its axis is I. It is allowed to roll on a surface without slipping. If its angular velocity is ω, then its K.E is:
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Total rolling K.E. = rotational K.E. + translational K.E.; for a solid cylinder I = 1/2 MR².
A body of mass m is moving in a circle of radius r with a constant speed v. The work done by the centripetal force in moving the body over the half circumference of the circle is:
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Centripetal force is always perpendicular to the instantaneous displacement.
If 'g' is the acceleration due to gravity at the surface of the earth, then the energy required to launch a satellite of mass m from the surface of the earth into circular orbit at an altitude of 2R, R being the radius of the earth, is:
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The orbit radius is 3R; compare the final orbital energy with the initial rest energy at the surface.
What remains constant when the earth revolves around the sun:
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The Sun's gravitational force is central, so Earth's angular momentum about the Sun is conserved.
A man in an elevator descending with an acceleration will conclude that his weight has:
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For downward acceleration, apparent weight is less than true weight.
