Rotational and Circular Motion

The centripetal force formula is F = mv^2/r, where m is mass, v is tangential velocity, and r is the radius of the circular path. This force is directed toward the center of the circle and keeps the object moving in circular motion. Option A has the division reversed, option C has incorrect variables, and option D is missing the squared velocity term.

Angular velocity (ω) is the rate of change of angular displacement with respect to time, measured in radians per second (rad/s). 'rad' alone is just the unit of angle, m/s is linear velocity, and m/s² is linear acceleration.

Angular speed (ω) is calculated as linear speed (v) divided by radius (r), giving ω = v/r. The formula relates the tangential velocity of a point on a rotating object to its distance from the center. Option A shows this relationship.

The Greek letter Theta (θ) is commonly used to represent angles (A) and angular position (B) in physics and mathematics. Angular velocity is typically represented by omega (ω), and angular frequency also uses omega, making options C and D incorrect.

To convert from radians per second to RPM, multiply by 60 (to get radians per minute) and divide by 2pi (since one revolution is 2pi radians). RPM = (w × 60) / (2pi). Option A would give radians per hour, while options C and D are incomplete conversions.

When an object moves to the diametrically opposite point on a circle, it travels half the circumference: distance = πR. Displacement is the straight-line distance from start to end, which is the diameter: 2R. Distance is path length traveled, displacement is shortest distance between points.

When a ball rotates in a horizontal circle, it has centripetal acceleration directed toward the center, provided by string tension. When the string breaks, this centripetal force vanishes. According to Newton's first law, the object continues in its current velocity direction - the tangent to the circle at the point of release. It does not fly radially outward (a common misconception), as that would require a force in that direction.

In uniform circular motion, acceleration is centripetal - it always points toward the center of the circular path. This acceleration is responsible for continuously changing the direction of velocity to maintain circular motion, not the tangent (which would be the velocity direction).

In circular motion, linear velocity v equals radius r multiplied by angular velocity w (v = rw). This relationship holds because angular velocity w is defined as the rate of change of angle, and the arc length traveled is r times the angle.

Glass has lower density than brass, so in air it experiences greater buoyant force. In vacuum, buoyancy disappears, reducing the upward force on the glass side more than the brass side, making the glass pan go down (decrease).

Decreases

Work done is zero because centripetal force is always perpendicular to the displacement of the particle. Since work = F × d × cos(θ) and θ = 90° throughout circular motion, cos(90°) = 0, making work done zero regardless of the number of revolutions completed.

Statement (1) is wrong. When a body is in circular motion, no work is said to be done by centripetal force. Statement (2) is wrong. The hand flour grinder is provided with a handle near its rim, because the perpendicular distance of the line of action of the force from the axis of rotation will be maximum to get the largest turning effect.

The filament in flagellum can rotate by 360 degrees.

The rate of change of angular displacement is called the angular velocity of the particles.