A cyclist accelerates from rest at a rate of 1.00 m/s². How fast will a point at the top of the rim of the tire (diameter = 68.0 cm) be moving after 2.75 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest—see Fig. 10–69.]

A wheel of diameter 40.0 cm starts from rest and rotates with a constant angular acceleration of 3.00 rad/s². Compute the radial acceleration of a point on the rim for the instant the wheel completes its second revolution from the relationship a_rad = v²/r.

A compact disc (CD) stores music in a coded pattern of tiny pits 10^-7 m deep. The pits are arranged in a track that spirals outward toward the rim of the disc; the inner and outer radii of this spiral are 25.0 mm and 58.0 mm, respectively. As the disc spins inside a CD player, the track is scanned at a constant linear speed of 1.25 m/s. What is the angular speed of the CD when the innermost part of the track is scanned? The outermost part of the track?

An electric turntable 0.750 m in diameter is rotating about a fixed axis with an initial angular velocity of 0.250 rev/s and a constant angular acceleration of 0.900 rev/s². What is the magnitude of the resultant acceleration of a point on the rim at t = 0.200 s?

How fast (in rpm) must a centrifuge rotate if a particle 8.0 cm from the axis of rotation is to experience an acceleration of 100,000 g’s?

On a 12.0-cm-diameter audio compact disc (CD), digital bits of information are encoded sequentially along an outward spiraling path. The spiral starts at radius R₁ = 2.5 cm and winds its way out to radius R₂ = 5.8 cm. To read the digital information, a CD player rotates the CD so that the player’s readout laser scans along the spiral’s sequence of bits at a constant linear speed of 1.25 m/s. Thus the player must accurately adjust the rotational frequency ƒ of the CD as the laser moves outward. Determine the values for ƒ (in units of rpm) when the laser is located at R₁ and when it is at R₂.

(III) A hammer thrower accelerates the hammer of mass 7.30 kg (Fig. 10–64) from rest within four full turns (revolutions) and releases it at a speed of 26.5 m/s. Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate the (linear) tangential acceleration (Ignore gravity).

<IMAGE>

A hammer thrower accelerates the hammer of mass 7.30 kg (Fig. 10–64) from rest within four full turns (revolutions) and releases it at a speed of 26.5 m/s. Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate the centripetal acceleration just before release. (Ignore gravity)

<IMAGE>

A hammer thrower accelerates the hammer of mass 7.30 kg (Fig. 10–64) from rest within four full turns (revolutions) and releases it at a speed of 26.5 m/s. Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate the net force being exerted on the hammer by the athlete just before release. (Ignore gravity).

<IMAGE>