Aball of radius r rolls on the inside of a track of radius r. if the ball starts from rest at the vertical edge of the track, find an expression for its speed (using terms g, r, and r) when it reaches the lowest point of the track, rolling without slipping? do not assume that the ball radius r is small in comparison to the track radius, r.

•• al and bert are jogging side-by-side on a trail in the woods at a speed of 0.75 m/s. suddenly al sees the end of the trail 35 m ahead and decides to speed up to reach it. he accelerates at a constant rate of 0.50 m/s2, while bert continues on at a constant speed. (a) how long does it take al to reach the end of the trail? (b) once he reaches the end of the trail, he immediately turns around and heads back along the trail with a constant speed of 0.85 m/s. how long does it take him to meet up with bert? (c) how far are they from the end of the trail when they meet?

Abug is 12 cm from the center of a turntable that is rotating with a frequency of 45 rev/min . what minimum coefficient friction is required so that the bug stays on the turntable?

Aparticle initially moving east with a speed of 20.0 m/s, experiences an acceleration of 3.95 m/s, north for a time of 8.00 s. what was the speed of the particle after this acceleration, in units of m/s? give the answer as a positive number.