Motion in a Circle

A powerful laser beam, with a very small divergence angle θ, is pointed at the Moon, a distance R away.

The value of R is in kilometres and the angle θ is in degrees.

Which of the following expressions gives the diameter, in metres, of the circle of light the laser produces on the Moon?

• 1.75 x 10^-5 Rθ

• 1.75 Rθ

• 1000 Rθ

• 5.73 x 10⁴ Rθ

A particle moves through a circular arc of length l and radius r in time t. Which expression gives its angular velocity about the centre of the circle?

• 1 / rt

• r / lt

• 2π / lt

• 2πr / t

The axis of rotation of a circular plate is through its centre and perpendicular to its plane. Two particles P and Q are on the plate. The distance P from the axis is twice that of Q.

At a given instant what is the value of (the linear velocity of P) / (the linear velocity of Q) ?

• 4

• 2

• 1/2

• 1/4

A communication satellite is moving at constant speed in a circular orbit about the Earth.

Which row in the table is correct about the momentum and kinetic energy of the satellite?

• A

• B

• C

• D

Which statement is correct about a particle moving in a horizontal circular path with constant angular velocity?

• The linear momentum is constant but the kinetic energy varies

• The kinetic energy is constant but the linear momentum varies

• Both kinetic energy and linear momentum are constant

• Both speed and linear velocity are constant

A body is moving in uniform circular motion.

Which row in the table correctly describes the linear velocity, angular velocity and linear acceleration of the body?

• A

• B

• C

• D

What is the mean angular speed of the minute hand of a clock?

• 1.4 x 10^-4 rad s^-1

• 1.7 x 10^-3 rad s^-1

• 5.2 x 10^-3 rad s^-1

• 1.0 x 10^-1 rad s^-1

A tape leaves a spool at a constant speed v and at a variable distance r from the centre of the spool.

How is the angular velocity of the spool related to r?

• It is proportional to 1 / r²

• It is proportional to 1 / r

• It does not depend on r

• It is proportional to r

A compact disc is rotating in a disc drive at a constant number of revolutions per second. A point on the disc, a distance r from the centre of rotation, is moving with speed v.

Which of the following graphs best illustrates the relationship between v and r?

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• 
• 

The given diagram illustrates a cylinder of radius 10.0 cm rolling at a constant angular velocity of 3/4 π rad s^-1 along a surface from left to right. The point X is initially at the bottom of the cylinder.

After 4.00 s, what is the displacement of X?

• 0.020 m

• 0.150 m

• 0.942 m

• 0.963 m