Free Rotational and Circular Motion MCQs with Answers

• A. equal to the radius
• B. equal to the diameter
• C. equal to the circumference
• D. one metre

Explanation: Since the arc length equals the radius times the angle in radians, an arc of one radius length subtends exactly one radian, about 57.3…

• A. pi over 2
• B. pi
• C. 2 pi
• D. 3 pi over 2

Explanation: A complete revolution of 360 degrees is 2 pi radians, so half a revolution is pi radians, roughly 3.14.

• A. v equals omega divided by r
• B. v equals r divided by omega
• C. v equals r omega
• D. v equals r squared omega

Explanation: In one second the body sweeps an angle omega, covering an arc of length r omega, so the linear speed is r omega with omega in radians per…

• A. 5 radians per second
• B. 31.4 radians per second
• C. 300 radians per second
• D. 1885 radians per second

Explanation: 300 revolutions per minute is 5 revolutions per second, and each revolution is 2 pi radians, so omega is 5 times 2 pi, which is 31.4…

• A. has zero acceleration
• B. is accelerating, because the direction of its velocity is continuously changing
• C. has a constant velocity
• D. experiences no net force

Explanation: Velocity is a vector, so changing its direction is a change in velocity even when the magnitude is fixed, and that change per unit time is…

• A. v squared divided by r, directed towards the centre
• B. v squared times r, directed away from the centre
• C. v divided by r squared, directed along the tangent
• D. zero, since the speed is constant

Explanation: The acceleration has magnitude v squared over r, equivalently r omega squared, and always points at the centre, which is why it is called…

• A. 200 N
• B. 2000 N
• C. 5000 N
• D. 10000 N

Explanation: The force is mv squared over r, which is 1000 times 100 divided by 50, giving 2000 N.

• A. a real force acting outwards on the passenger
• B. the reaction to the passenger's weight
• C. an apparent force arising because the passenger is in a rotating, non inertial frame
• D. always larger than the centripetal force

Explanation: In the ground frame the passenger simply continues in a straight line by inertia while the bus turns beneath them, so no outward force is…

• A. the mass of the car only
• B. the speed and the radius of the curve
• C. the weight of the passengers
• D. the width of the road

Explanation: Setting the horizontal component of the normal force equal to mv squared over r gives tan theta equal to v squared over rg, and the mass…

• A. T equals omega over 2 pi
• B. T equals 2 pi omega
• C. T equals 2 pi over omega
• D. T equals omega squared

Explanation: One complete revolution covers 2 pi radians, so the time taken is 2 pi divided by the angular speed.

• A. its mass only
• B. its mass and how that mass is distributed about the axis of rotation
• C. its angular speed
• D. the torque applied to it

Explanation: Moment of inertia is the sum of each mass element multiplied by the square of its distance from the axis, so moving mass further out…

• A. the angular speed increases, because the moment of inertia decreases and angular momentum is conserved
• B. the angular speed decreases
• C. the angular momentum increases
• D. nothing changes

Explanation: With no external torque the angular momentum, the product of moment of inertia and angular speed, stays constant, so reducing the moment…

• A. I alpha
• B. I omega
• C. m v r squared
• D. half I omega squared

Explanation: Angular momentum is the moment of inertia multiplied by the angular speed, the rotational analogue of linear momentum mv.

• A. the vacuum of space
• B. its own centrifugal force
• C. the gravitational pull of the Earth acting as the centripetal force
• D. the thrust of its engines

Explanation: Gravity supplies exactly the inward force needed to bend the satellite's straight line motion into a circle, so no engine is required once…

• A. 1 hour
• B. 12 hours
• C. 24 hours
• D. 365 days

Explanation: To stay above the same point on the equator the satellite must complete one orbit in exactly the time the Earth takes to rotate once…

• A. half m v squared
• B. I omega
• C. half I omega squared
• D. I alpha

Explanation: Replacing mass with moment of inertia and linear speed with angular speed in the familiar expression gives half I omega squared.

• A. fly radially outwards from the centre
• B. move along the tangent to the circle at the point of release
• C. fall straight down at once
• D. spiral outwards while slowing down

Explanation: With the centripetal force gone, no force acts horizontally and Newton's first law takes over, so the stone keeps the velocity it had at…

• A. v equals the square root of rg
• B. v equals rg
• C. v equals zero
• D. v equals the square root of 2rg

Explanation: At the critical speed the normal reaction falls to zero and gravity alone provides the centripetal force, so mg equals mv squared over r…

• A. metres
• B. radians
• C. metres per second
• D. newtons

Explanation: The radian is the SI unit of angle, and because it is defined as a ratio of two lengths it is dimensionless, which is why the formula v…

• A. twice the angular speed and the same linear speed
• B. the same angular speed and twice the linear speed
• C. half the angular speed
• D. the same linear speed

Explanation: Every point on a rigid rotating body sweeps the same angle in the same time, so the angular speed is common to all of them.