Circular Motion

Question 1

Define angular displacement

Answer 1

Angle an object makes with respect to a reference time

Question 2

Define radian

Answer 2

Angle subtended by an arc length equal to the radius of the arc

Question 3

Define angular velocity

Answer 3

Rate of change of angular displacement with respect to time

Question 4

Use Newton’s laws of motion to explain why a body moving with uniform speed in a circle must experience a resultant force

Answer 4

Resultant force:
By N1L, body is not moving in a straight line but in a circular path, so there must be a resultant force to change its direction. Direction of motion is constantly changing -> must have an acceleration. N2L -> body must experience a resultant force in the same direction as the acceleration.

Question 5

Use Newton’s laws of motion to explain why there is acceleration in a body traveling at a constant speed in a circular path even though the speed is constant.

Answer 5

Velocity of the body changes along a circular path.
By N1L, this requires and external force to act on the body.
Since the centripetal acceleration is pointing to the center of circle and perpendicular to the instantaneous velocity, by N2L, it has no component along the path, hence speed is constant.

Question 6

How does frictional force enable a car to travel in the same horizontal circular path at a lower speed?

Answer 6

The horizontal component of static friction acts away from the direction of centripetal force, resulting in a smaller magnitude of centripetal force, permitting the car to move on the banked surface in uniform circular motion with a slower speed.

Question 7

Show all derivations for centripetal force.

Answer 7

Fc = mac= m(v²/r) = mrω² = mvω

Question 8

Derive angle of mass moving in circular motion

Answer 8

cosθ = mg
sinθ = m(v²/r)
tanθ = v²/rg

Question 9

Centripetal force on an object that is on the top during uniform circular motion

Answer 9

T(top) + mg = m(v²/r)